-    /"  UC-NRLF 


15    772 


EINGIME  AND  BOILER 
DESIGN 


HOFFMAN 


A  COUESE  OF  INSTRUCTION 


ENGINE  AND   BOILEE   DESIGN 


ARRANGED    FOR 


STUDENTS    OF    THE    SENIOR    CLASS 

PURDUE    UNIVERSITY 

LAFAYETTE,   IND. 


BY 


J.  D.  HOFFMAN.  M.  E. 

Associate  Pi-ofessor  in  Engineering  Design 


PRESS  OF    BURT-TERRY- WILSON     CO 
LAFAYETTE.    INO, 


UtNEHAL 

•| 


Copyright,  1906, 

BY 
JAMES  D.  HOFFMAN. 


STEAM    ENGINE    DESIGN 

REFERENCE  LIST. 


Young — Steam  Engine  and  Boiler  Notes 
and    Problems. 

Hutton — Mechanical  Engineering  of  Pow- 
er Plants. 

Whitham — Steam  Engine  Design. 
Klein — Steam  Engine  Design. 

Rigg — Practical    Treatise    on    Steam    En- 
gines. 

Rankine — Steam  Engines. 


Barr — Current    Practice    in    Engine    Pro- 
portions. 
Cotterill — The   Steam   Engine. 


Unwin — Elements 
Vol.  II. 


of     Machine     Design, 


Thurston — A  'Manual  of  the  Steam  Engine. 

Reuleaux — The  Constructor. 

Holmes — The  Steam  Engine. 

Kent — Mechanical  Engineers'  Pocket  Book. 


In  connection  with  the  above,  look  up  the  numbers  of  the  Engineering  Index;  they  come  monthly 
and  give  references  from  over  two  hundred  engineering  papers.  Three  bound  Volumes  of  this  index 
have  appeared,  the  last  one  in  1902.  These  volumes  contain  a  vast  amount  of  information  concerning 
references  on  the  design  of  steam  engines. 

In  the  following  notes,  reference  is  frequently  made  to  the  "Manufacturers  Average"  (M.  A.). 
These  references  are  taken  from  a  thesis  presented  in  1904  by  Mr.  F.  A.  Berger  on  "The  Comparison 
and  Development  of  Formulae  for  the  Design  of  High  Speed  Steam  Engine  Details."  This  investiga- 
tion has  not  only  summed  up  existing  formulas,  but  has  averaged  the  standard  sizes  of  the  parts  in  en- 
gines of  the  various  types. 

PROBLEMS  IN  HIGH-SPEED  STEAM  ENGINE  DESIGN. 

In  developing  a  design  of  this  kind  it  is  not  required  that  each  man  keep  an  accurate  record  of  all 
the  work  on  the  individual  parts  made  by  the  other  designers.  It  will  be  advisable,  however,  to  keep 
in  as  close  touch  as  possible  with  their  work.  To  accomplish  this,  the  following  problems  should 
be  worked  out  by  every  member  on  the  design  and  submitted,  with  such  other  notes  and  remarks  on 
the  design  as  he  deems  important,  at  the  end  of  the  time  when  the  design  shall  be  finished  and  at  such 
other  times  during  the  progress  of  the  work  as  they  shall  be  called  for  by  the  instructor. 

Sizes  shall  be  calculated  where  possible  and  wherever  such  calculated  sizes  are  departed  from, 
both  calculated  and  accepted  sizes  should  be  given.  It  is  urged  that  frequent  reference  be  made  to 
late  catalogues  and  other  information  to  check  up  the  work  with  current  practice. 

PROBLEM  i.     Determine  the  size  (diameter  and  stroke  )  of  the  engine  cylinder  for  your  assigned 

horse  power. 
PROBLEM  2.     Estimate  the  horse  power  of  the   engine  at    i-io,    1-4  and   7-10   cut-off,   using  the 

planimcter  for  the  M.  E.  P. 

PROBLEM  3.     Estimate  the  weight  of  the  reciprocating  parts  by  Barr's  formula. 
PROBLEM   4.     Estimate  the  force  necessary  to  accelerate  the  reciprocating  parts  with  the  engine 

on  first,  head  end  dead  center ;  second,  crank  end  dead  center. 

PROBLEM  5.     Determine  the  coefficient  of  fluctuation  of  energy  for  i-io,   1-4  and  7-10  cut-off. 
PROBLEM  6.     Estimate  the  number  of  foot  pounds  of  energy  that  must  be  taken  up  and  given  out 

by  the  flywheel  at  i-io,  1-4  and  7-10  cut-off. 

PROBLEM  7.     In  calculating  the  flywheel  for  this  engine  estimate  the  width  of  belt, 

(a),  if  single   belt  is  used, 
(b),  if  double  belt  is  used. 

State  size  of  belt  adopted  and  give  width  of  face  of  flywheel. 


197986 


PROBLEM     8.     Determine  the  weight  of  the  flywheel  and  the  thickness  of  the  rim. 

PROBLEM     9.     Determine  the  diameter  of  the  crank  shaft. 

PROBLEM  10.     Determine  the  dimensions  of  the  crank  pin;  projected  area,  length  and  diameter. 

PROBLEM   n.     Determine  the  dimensions  for  the  wrist  pin;  projected  area,  length  and  diameter. 

PROBLEM    12.     Determine  the  sections  of  the  crank  arm  at  the  pin  and  at  the  center  of  the  shaft. 

PROBLEM   13.     Determine  the  section  of  the  connecting  rod  at  the  wrist  pin  end,  regarding  the  rod 

as  in  tension. 
PROBLEM   14.     Estimate  the  ratio  of  the  given  load  on  the  connecting  rod  to  that  load  that  would 

start  flexure  considering  the  rod  as  a  column. 

PROBLEM   15.     Determine  the  area  of  the  bearing  surface  of  the  cross  head. 
PROBLEM   16.     Determine  the  diameter  of  the   piston  rod. 
PROBLEM   17.     Estimate  the  ratio  of  the  given   load  on  the  piston  rod  to  the  load  that  would  start 

flexure,  assuming  the  rod  to  be  pin  and  square  ended.     Assume    also  /    =    -f 

length  of  stroke. 

PROBLEM  18.     Determine  the  width  of  the  face  of  the  piston. 

PROBLEM  19.     Determine  the  thickness  of  the  cylinder  wall ;  also  that  of  the  cylinder  head. 
PROBLEM  20.     Determine  the  number  and  diameter  of  studs  for  the  cylinder  head. 
PROBLEM  21.     Determine  the  following  steam  passages: 

(a),  steam  pipe;  area  and  diameter, 
(b),  exhaust  pipe;  area  and  diameter, 
(c),  cylinder  ports;  area,  length  and  width. 


NOTES  ON  THE  DESIGN  OF  HIGH  SPEED  STEAM  ENGINES. 

The  terms  lou>  speed  and  high  speed  as  applied  to  steam  engines  relate  to  the  revolutions 
per  minute.  It  is  usually  understood  that  low  speed  engines  have  from  100  to  200  R.  P.  M.  and  high 
speed  engines  from  200  to  350  R.  P.  M. 

Piston  Speed; — The  piston  speeds  of  stationary  engines  vary  from  500  to  700  F.  P.  M.  The 
lower  speeds  are  found  on  the  smaller  engines,  say  from  10  to  30  H.  P.  The  piston  speeds  are  about 
the  same  on  low  and  high  speed  engines  of  the  larger  sizes,  except  where  designed  for  special  work ; 
for  illustration :  a  13"  x  15"  high  speed  engine  runs  at  about  250  R.  P.  M.,  and  an  18"  x  36"  Corliss 
runs  at  about  100  R.  P.  M.  each  having  approximately  600  F.  P.  M.,  piston  speed.  The  average  of 
a  number  of  actual  cases,  however,  shows  a  speed  of  585  F.  P.  M. 

Revolutions  Per  Minute: — The  average  of  a  number  of  engines  shows  the  following:  50  H.  P., 
290  R.  P.  M. ;  100  H.  P.,  260  R.  P.  M. ;  150  H.  P.,  230  R.  P.  M. ;  a  decrease  of  30  R.  P.  M.  for  each 
increase  of  50  H.  P. 

Theoretical  Indicator  Card: — In  beginning  the  design  of  a  steam  engine  the  first  thing  to  be  con- 
sidered is  the  theoretical  indicator  card.  In  order  to  obtain  this  a  few  assumptions  must  be  made, 
namely:  boiler-pressure,  cut^oTT,  compression,  admission,  release,  clearance  and  back  pressure. 

Boiler  Pressure: — This  ranges  in  practice  from  85  to  125  pounds  gauge  pressure.  Very  high 
steam  pressures  are  not  economical  in  single  cylinder  engines,  but  are  used  in  multiple  cylinders  and 
condensing  engines.  Current  practice  seems  to  favor  90,  95  and  100  pounds  gauge  for  the  50,  100 
and  150  H.  P.  single  cylinder  non-condensing  engines,  respectively. 

Cut-Off: — Cut-off  varies  from  10%  to  70%  of  the  stroke,  the  normal  rating  being  at  25%.  It 
will  be  well  in  this  work  to  assume  three  cut-offs,  10,  25  and  70%,  so  as  to  permit  of  satisfactory  com- 
parison. 


Compression:  —  This  serves  two  purposes,  to  heat  up  the  cylinder  and  to  cushion  the  reciprocat- 
ing parts.  We  will  not  consider  theoretical  values  here,  but  will  take  an  average  obtained  from  an 
analysis  of  a  number  of  engines,  as  follows  :  — 

10%   cut  off  ......  45%  Compression. 

25%   cut  off  ......  34%  Compression. 

70%  cut  off  ......  12%  Compression. 

Admission  and  Release:  —  Admission  and  release  depend  upon  cut-off  and  compression  and  can  not 
be  arbitrarily  assumed.  The  following  is  au  average  taken  from  the  analysis  previously  meii 
tioned. 

10%   cut-off.  8%   admission  56%    release. 

25%    cut-off  3%   admission  67%  release. 

70%   cut-off  o%   admission  92%  release. 

It  seems  scarcely  necessary  to  make  any  assumption  regarding  admission  and  release  on  the 
theoretical  cards,  since  no  values  could  be  assigned  to  fulfil  the  average  'conditions  as  indicated  for 
the  three  cut-offs.  Some  designers  take  admission  and  release  at  the  ends  of  the  stroke.  In  either  case 
errors  will  be  involved,  but  it  is  altogether  probable  that  the  errors  will  be  less  when  admission  and 
release  are  considered  as  given  in  the  table. 

Clearance:  —  Clearance  may  be  divided  into  two  parts:  (a),  between  the  piston  and  cylinder 
head,  this  varies  from  %"  to  %"  for  rough  castings,  and  116-"  to  J-"  for  finished  castings;  (b), 
steam  passage.  Total  clearance  will  vary  from  6  to  12%  of  the  steam  volume  per  stroke  in  high  speed 
engines.  This  may  be  taken  at  8%.  Low  speed  engines  will  have  much  less  percentage  of  clearance, 
some  times  as  low  as  2%  of  the  steam  volume  per  stroke. 

Back  Pressure:  —  Assume  back  pressure  as  follows: 

Non-condensing  2  to  4  pounds  gauge;  17  to  19  pounds  absolute. 
Condensing  2  to  4  pounds  absolute. 

Cylinder  Size:  —  Having  been  assigned  the  horse  power  of  the  engine  to  be  designed,  the  first 
operation  is  to  find  the  diameter  of  the  cylinder  from  the  formula: 

P  V 

H.  P.  =  -  (i) 

33000 

where  P  =  M.  E.  P.  X  Area  of  piston  and  V  =    Piston  speed  in  F.  P.  M. 
Find  M.  E.  P.  from  the  formula   (2)   and  substitute  in  (i) 


M.  E.  P.  =  =  p       i+frg-*'     .  _  back  pressure.  (2) 

f 

where  p  ==  absolute  initial  pressure,  and  r  =  number  of  expansions.     In  obtaining  r,  it  will  not  be 
necessary  to  consider  clearance. 

NOTE.  —  Formula  (2)  is  an  approximate  formula  which  gives  results  entirely  satisfactory  for  the 
determination  of  the  cylinder  diameter.  After  the  theoretical  cards  have  been  drawn  the  areas  should 
oe  taken  with  a  planimeter  and  the  M.  E.  P.  for  the  three  cut-offs  computed  from  these  areas.  It  will 
be  of  interest,  then,  to  compare  the  results  obtained  in  the  two  ways. 


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Another  approximate  rule  for  finding  the  cylinder  diameter  is    H.  P.  =  ^4  D"  (3) 

On  the  basis  of  the  manufacturers'  rating  this  formula  would  become  H.  P.  =  %  D2.  This 
rating  is,  however,  below  the  average  engine  performance. 

After  obtaining  the  cylinder  diameter  D,  assume  the  length  of  stroke  L,  and  the  number  of 
revolutions  per  minute  N,  such  that  L  N  •  -  Piston  speed  in  F.  P.  M. 

Manufacturers'  average:     L   =    1.122  D   =   say  i*/s  D. 

In  selecting  the  cylinder  sizes  the  following  ratios  may  be  of  value. 

7",     8",     9",  10"  and  11"  x  10"  n",  12",  13",  14"  and  15"  x  15" 

10",  11",  12",  13"  and  14"  x  12"  14",  15",  16",  17"  and  18"  x  16" 

12",  13",  14",  15"  and  1 6"  x  14" 

Theoretical  Diagrams  Sheet: — In  planning  this  sheet,  Plate  C  -  132  may  be  used  as  a  guide. 
Draw  the  Force  Diagram  at  the  top  to  any  convenient  scale,  then  draw  the  Theoretical  Indicator  Cards 
for  each  of  the  three  cut-offs  and  combine  the  forward  and  backward  cards,  simultaneously  produced, 
into  the  Effective  Steam  Pressure  Cards. 

To  obtain  the  diagram  representing  the  inertia  of  the  reciprocating  parts,  i.  e.,  piston,  piston  rod, 
cross-head  and  one  half  of  the  connecting  rod,  it  will  be  necessary  to  estimate  the  weight  of  these 
parts.  This  is  commonly  done  by  Barr's  formula : 

W  •-  -  1,860,000  j~-  (4) 

where  W  =  weight  in  pounds,  D  =  diameter  of  cylinder  in  inches,  L  =  length  of  stroke  in  inches,  N 
=  R.  P.  M. 

The  M.  A.  seems  to  run  somewhat  greater  than  the  above  and  is  represented  by  the  formula: 

i  ,900,000  D 
W=~   -^~ 

After  the  value  of  W  is  obtained  it  is  then  substituted  in  the  formula : 

sin2  e  /2  cos2  e 


where  F  -  -  force  necessary  to  accelerate  the  reciprocating  parts,  W  -  weight  of  reciprocating  parts 
in  pounds,  v  =  velocity  of  crank  pin  in  F.  P.  S.',  /  =  length  of  connecting  rod  in  feet,  r  =  Radius  of 
crank  in  feet,  0  =  Crank  angle  with  the  horizontal,  g  =  32.2. 

may  be  taken  from  54  to  %. 


I 

In  applying  (5)  it  will  be  necessary  to  solve  for  0  =  o°  and  0  =  180°. 
For  6  =  o°  the  acceleration  is  negative  and  falls  below  the  horizontal  line,  for  6  =  180°  the 
acceleration  is  positive  and  is  shown  above  the  line.  Since  the  inertia  card  on  the  return  stroke  is  ol 
the  same  size,  representing  no  loss  of  energy,  the  positive  and  negative  forces  become  negative  and  pos- 
itive, respectively,  as  shown.  This  gives  two  points  in  the  inertia  curve,  i.  e.,  the  extremes.  The 
formula  can  then  be  solved  for  intermediate  values  of  6  between  o°  and  180°  and  an  accurate  curve 
produced ;  this,  however,  has  been  found  to  approximate  to  the  arc  of  a  circle  passing  through  the  ex- 
tremes as  found,  and  p,  a  point  on  the  .r,  axis  where  the  acceleration  passes  from  negative  to  positive  and 
vice  versa.  This  point  p  will  lie  at 

.46  stroke  when  r  —  /  =  % 

.45  stroke  when  r 

.44  stroke  when  r 

After  locating  the  points  as  stated,  pass  arcs  of  circles  through  them  and  these  arcs  will  repre- 
sent the  acceleration  curves. 

The  curves  representing  the  forces  on  the  twist  pin  are  next  plotted  by  combining  the  effective 
steam  pressure  cards  and  the  inertia  cards.  It  will  be  noticed  that  the  effect  of  the  inertia  card  is  to 
round  up  the  final  card  and  more  nearly  equalize  the  effective  forward  forces. 

The  forces  representing  the  tangential  pressures  on  the  crank  pin  are  obtained  by  multiplying 
the  forward  forces  on  the  wrist  pin  by  the  -values  A  N  -f-  r  given  in  the  following  table.  Concerning 
A  N  ~^r  see  "Stahl  &  Wood,"  Elementary  Mechanism,  Page  196;  also  Steam  Engine  &  Boiler  Notes 
(Young.) 


Values  of  A  N  -:    / . 


Piston  Position 


.00  

oo 

•05  

47 

.10  

'  >4 

.20  

84 

•30  

95 

.40  

I.OI 

•50  

I.OI 

.60  

97 

•7°  

88 

.80  
.go.. 

76 
54 

•95 39 

i  .00 oo 


75 

.OO 
.48 
•65 

.86 

.96 

i. 02 

I.OI 

•97 
.87 

•74 
•52 
•36 
.00 


.00 
•50 
.67 
.88 
.98 
1.03 

1.02 
.96 

•85 

.72 

•50 
•36 
.OO 


For  any  other  ratio  of  r  -f-  /  the  value  A  N  -=-  r  can  be  found  either  analytically  or  graphically. 

Locate  the  corresponding  positions  of  the  crank  pin  on  the  crank  circle,  .05,  .1,  .2,  .3  etc.,  draw 
indefinite  radial  lines  through  them,  lay  off  these  products  outside  the  crank  circle  and  through  the 
points  obtained  draw  the  irregular  curve  representing  the  locus  of  the  tangential  forces  exerted  on  the 
crank  pin. 

The  rectified  tangential  curves  are  obtained  by  drawing  the  x  axis,  the  length  of  the  half  circum- 
ference of  the  crank  circle,  and  at  the  points,  .05,  ,i,  .2,  .3  etc.,  erect  perpendiculars  of  equal  length  to 
the  radial  lines  outside  the  circle  in  the  tangential  pressure  diagram  and  through  these  extremities  draw 
the  rectified  arc.  Find  the  area  of  each  half  of  the  enclosed  figure  and  divide  by  the  length.  This  will 
give  the  average  height  of  card,  or  the  mean  tangential  pressure  line.  See  also  Whitham,  page  199; 
Heck,  Notes  Supplementing  Holmes,  Page  23;  Holmes,  Page  196;  Unwin,  Page  173;  Marks,  Page 
120;  Klein,  Page  63. 

Fly  Wheel: — The  lack  of  uniformity  in  the  turning  effort  at  the  crank,  produces  fluctuations  of 
speed  in  the  engine.    The  way  in  which  this  may  be 
largely  overcome  is  to  design  a  fly  wheel  of  suf- 
ficient weight  to  absorb  and  control  these  fluctua- 
tions.    In  the  steam  engine  notes  the  formula  for          , 
the  weight  of  the  fly  wheel  is  given  as  / 


W  = 


KEG 


(6) 


where 

W  =  weight  of  the  wheel  in  pounds. 


IV"      


bed 


d  q  q'  d' 


B  =  energy  of  one  revolution  in  foot  pounds  FIG.  i. 

G  =    32.2 

n  =  coefficient  of  fluctuation  of  speed,  taken     at  i-ioo  to  1-150  for  high  speed  engines.    For  elec- 
tric lighting  the  higher  figure  would  be  used. 

v  =  velocity  of  the  fly  wheel  rim  in  F.  I'.  S.  The  velocity  of  the  fly  whel  rim  would  be  the 
same  as  that  assumed  for  the  belt  which  may  be  taken  at  4,000  F.  P.  M.  Practice  varies  on 
this  point  from  3,000  to  6,000  F.  P.  M.  The  maximum  efficiency  of  a  belt  is  obtained  in 
practice  at  about  5,000  F'.  P.  M.,  but  the  ordinary  practice  for  high  speed  work  is  about  as 
stated,  with  smaller  engines  say  30  to  50  H.  P.,  some  below;  and  larger  ones,  say  100  to 
150  H.  P.,  some  above  this  figure. 

*These  two  areas  are  not  equal,  b  c  d  is  commonly  used.  The  suggestion  is  made  that  the  great- 
est fluctuation  should  be  taken  and  if  the  two  deficiencies  H  q  q'  d'  be  greater  than  b  c  d,  it  should  be 
used  instead. 


In  selecting  v  it  would  be  well  to  consider  what  is  the  best  diameter  for  the  wheel.    The  (M.  A.) 


gives  D  =  .0235  V  H.  P.  X  N  (7) 

where    ./V  =  R.  P.  M.  and  D  =  diameter  in  feet. 

The  assumed  velocity  can  then  be  checked  up  with  the  above  before  substituting  it  in  the  form- 
ula for  the  weight  of  the  wheel. 

The  weight,  as  found,  would  naturally  be  that  of  the  entire  wheel  as  though  it  were  all  fixed  in 
the  rim.  This  is  not  theoretically  correct  since  the  arms  have  considerable  weight,  but  in  practice 
it  is  generally  taken  in  this  way. 

Other  Formulas  for  Weight  of  Fly  Wheel. 

pj  p  I  D  =  Diameter  of  wheel  in  inches. 

Barr  :—  W   =   833,000,000,000         '     ' 

[  N  =  R.  P.  M. 

UP  f  D  ^"Diameter  of  wheel  in  inches. 

Thurston:  —  W   =   960,000,000,000          '  J  N  =  R.  P.  M. 

[  where  M.  E.  P.  is  not  less  than  30. 
~2  ,  f    D  =  diameter  of  cylinder  in  inches. 

L  =  stroke  in  inches. 
btanwood:  —  W  =  1,000,000  -  in        A-  r     u    i  •     r 

Dt  =  diameter  of  wheel  in  feet. 


Ar2 

1 


N  =  R.  P.  M. 


^87  sS?  zoo  K  n  V  H  P  (n  -—  variation  of  speed  say  1-50  to  i-ioo. 

Whitham  :-W  =  \D  =  diameter  of  rim  in  feet. 

[N  =  R.  P.  M. 

„      _   excess  of  turning  effort  over  resistance 
whole  crank  effort  during  one  stroke. 

K  X  H  P  ff   —  coefficient  of  unsteadiness  =  1-50  to  i-ioo. 

Klein  :—  W  =  388,000,000       ,  n,    '  \  D    -  diameter  of  wheel  in  feet. 

(N  =  R.  P.  M. 

_         excess  of  power  or  resistance  during  any  phase 
total  power  exerted  during  one  revolution. 
(M.  A.)  :  —  W  —  H.  P.  (.05  TV  +  10)       N  =  R.  P.  M. 

With  a  given  velocity  of  the  belt  and  an  assumed  working  strength  of  the  belt  per  square  inch  of 
section,  the  next  operation  is  to  decide  on  either  single,  double  or  triple  belt  and  solve  for  the  width. 

Concerning  the  working  strength  of  the  belt  mucn  might  be  said,  and  many  references  might  be 
cited,  chiefly  those  in  Kent,  Pages  876-887.  These  references  and  others  that  might  be  given  show 
such  n  lack  of  uniformity  that  it  becomes  largely  a  matter  of  the  judgment  of  the  designer.  Tests  of 
belting  show  an  ultimate  strength  of  about  4,ooo*[]";  allowing  a  factor  of  safety  of  10,  we  would 
have  400  8[]"  as  a  maximum  working  strength.  This  figure  is,  however,  seldom  reached.  The  extremes 
of  practice  for  the  working  strength  per  square  inch  of  section  are  about  250  to  400,  which  agrees  in 
practice  with  a  tractive  force  of  from  180  to  290  pounds  per  square  inch  of  section.  Kent  seems  to  fa- 
vor a  tractive  force  of  275  pounds  per  square  inch  of  section  which  is  equivalent  in  a  double  belt  to 
about  86  pounds  per  inch  of  width.  This  figure  seems  to  give  results  that  agree  well  with  current 
practice  in  high  speed  engine  work.  Concerning  the  thickness  of  the  belt  it  may  be  said  that  for 
power  work  on  engines  exceeding  50  H.  P.  a  double  belt  would  be  preferred.  The  following  thicknesses 
may  be  accepted  for  belting:  — 

single  belt  ..............  3-16" 

double  belt  .............  5-16" 

triple  belt  ...............  7-16" 

Taking  the  formula  P  V  -±-  33000  =  H.  P.  we  can  obtain  the  total  tractive  pull  P  on  the  belt, 
then  knowing  the  tractive  force  of  the  belt  per  inch  in  width,  the  width  in  inches  of  belt  can  be  obtained. 
Having  the  width  of  the  belt,  the  width  of  the  pulley  face  is  obtained  by  adding  from  l/2  to  2  inches 
to  the  belt  width. 


Another  very  satisfactory  formula,  if  it  is  desired  to  take  into  account  the  centrifugal  tension  and 
the  arc  of  contact  of  the  belt,  is  that  given  in  Kent,   Page  878,  by  Nagle. 


H.  P.  =  C  V  t  w 


(f  —  .012 

550 


where  C  =  I  —  iO--007D8^  a 

a    =  degrees  of  belt  contact. 

$  =  coefficient  of   friction   generally   taken  at  from  .3  to  .4 

ty  =  width  of  belt  in  inches. 

t     =  thickness  of  belt  in  inches. 

V  =  velocity  in  feet  per  second. 

f    =  stress  on  belt  per  square  inch  of  section. 

f   =  275  for  laced  belts. 

f     -  400  for  lapped  and  rivetted  belts. 

Table  of  Values  of  C  =  i  —  iO-00758*a 
For  different  arcs  of  contact. 


Take 


$  =  Coeff 

of 
Friction. 

15 
20 

25 
30 

35 
40 

45 

55 

60 

100 


DEGREES  OF  CONTACT  =  a 


90 

IOO 

no 

I2O 

I3<> 

140 

150 

160 

170 

180 

200 

.210 

.230 

.250 

.270 

.288 

•307 

•329 

•342 

•359 

•376 

.408 

.270 

•295 

.318 

•342 

•364 

.386 

.408 

.428 

.448 

.467 

•5°3 

•325 

•354 

.381 

.407 

•432 

•457 

.480 

•503 

•524 

•544 

-582 

•376 

.408 

438 

.467 

•494 

.520 

•544 

.567 

•590 

.610 

.649 

•423 

•457 

.489 

.520 

•548 

•575 

.600 

.624 

.646 

.667 

•7°5 

.467 

.502 

.536 

.567 

•597 

.624 

.649 

•673 

•695 

•715 

•753 

.507 

•544 

•579 

.6lO 

.640 

.667 

.692 

•715 

•737 

•757 

•792 

•572 

.617 

.652 

.684 

•713 

•738 

•763 

.785 

•805 

.822 

•853 

.610 

.649 

.684 

•715 

•744 

.769 

.792 

•713 

.832 

.848 

.877 

•792 

.825 

•853 

•877 

.897 

•9i3 

.927 

•937 

•947 

•956 

.969 

The  (M.  A.)  for  width  of  fly  wheel  pulley  rims  is  W    -  i.  35  V  H.  P. 

In  determining  the  thickness  of  the  pulley  rim   having  given  the  width,  the  following  formula  will 
be  sufficiently  accurate. 

W    =    .26     7T    W     (D—t)     t 

where  D  =  diameter  of  pulley  in  inches. 
t    =  thickness  of  rim  in  inches. 
W  =  weight  of  pulley  in  pounds. 
w  =  width  of  rim  in  inches. 
(M.  A.),  t  =  .27  D  +  .5"  where  D  =  diameter  in  feet. 

Some  standard  pulley  sizes: — 
Diameter  in  inches 

36" : 

42" 

48" 

54" 

60" 

66" 

72" 


Face  in  inches. 

.  6y2"....  sy2 


.  8y2".... 
.10/2".... 


,12/3"....: 


The  shape  of  the  arm  section  is  then  selected  and  the  arm  calculated  as  a  beam  under  flexure.    If 
this  section  is  oval  as  shown  in  the  figure,  the  formula  becomes 


PL 

N 


=   -05  b*  f 


FIG.  2. 


where  P  =  Tractive  force  of  belt 

f    =  Allowable  fibre  stress  of  the  metal,  say 
2000«"" ; 

N  =r  Number  of  arms. 

b  =  Breadth  of  arm  at  center  of  wheel  if 

projected  to  that  point. 

_The  breadth  and  thickness  of  the  arm  at  the 
rim  may  be  taken  at  approximately  2-3  of  the  hub 
sizes. 


For  the  diameter  of  the  hub  a  very  common  practice  is  to  take  a  value  equal  to  twice  the  diameter 
of  the  shaft.   (=  2  d) 

For  the  size  of  the  key  use : — 


for  a  six  inch  shaft  to 


w  = 


-  for  a  two  inch  shaft. 
I    4 


(2  "\          \ 

—  w  to  —  tti  )    for  a  six  inch  shaft 
3  4       ' 


f 

_c 
T                                           .» 

4  •              i 

H^ 

w 

FIG.  3. 
li  =   (  —   w  to  w  }    for  a  two  inch  shaft. 


Bed: — No  rules  can  be  laid  down  concerning  the  weight  of  the  engine  bed.     It  seems  to  vary 
between  20  and  35  pounds  per  horse  power. 

Shaft: — In  every  crank  shaft,  no  matter  if  the 
engine  is  side  crank  or  center  crank,  two  forces 
are  acting :  ( i )  A  twisting  movement  T  due  to  P  r, 
(2),  A  bending  movement  M  due  to  P  a.  The 
two  can  be  reduced  to  an  "equivalent  twisting  move- 
ment T  as  shown  by  Low  &  Bevis,  Page  95,  and 
\Yhitham,  Page  245. 


r  =  M+V~ 

then  find  the  diameter  from 
d=  1.72  ll~ 


+   T1 


Kent : — 


FIG.  4. 
.43  D  for  long  stroke  engines. 


(9) 


(10) 


A  good  value  for  /  in  such  cases  is  8,000. 

The  above  gives  safe  values  except  with  very 
heavy  fly  wheels  where  the  bending  due  to  the 
weighr  of  the  fly  wheel  must  be  taken  into  account. 

Other  formulas  are  given  as  follows : 


•D  =  diameter  of  cyl.  in  inches. 


=  .40  D  for  short  stroke  engines  j 
I.  C.  S. : d  —  .44  D  +  y2" D  =  diameter  of  cyl.  in  inches. 

9 


Barr;  — 


_ 

d  =  7.3  Al   H-  P-  for  hi 

*  £.  P.  M. 


high  speed  engines. 


3 


(ID 


d  =  6.8  „/  -^  P-'  for  low  speed  enjnnes. 


(M.  A.)  :  —  d  =  .0053  D  P.  where  D  =  diameter  of  cylinder  in  inches  and  P  =  boiler  pressure 
(gauge.) 

The  formulas  by  Barr  seem  to  give  the  most  universal  satisfaction. 

Crank  Pin:  —  The  crank  pin  should  be  designed,  first,  to  avoid  heating;  second,  for  strength;  third, 
for  rigidity.  As  a  matter  of  fact  the  first  of  these  factors  is  the  most  important  one  and  is  generally 
considered  first.  Experience  has  shown  that  the  heat  dissipated  is  proportional  to  the  projected  area 
of  the  pin  and  hence  the  equation  C  d  I  =  P  A.  or 

PA 


where  C  =  pounds  pressure  per  square  inch  projected  area  allowed,  d  =  diameter  of  pin  in  inches, 
/  =  length  of  pin  in  inches,  P  =  mean  effective  pressure  in  pounds  per  square  inch  of  piston,  and  A  = 
area  of  piston  in  square  inches. 

Current  engine  practice  (See  Trans.  A.  S.  M.  E.,  Vol.  17,  page  124)  has  shown  that  the  projected 
areas  in  a  large  number  of  engines  averaged  according  to 

d  I  =  .22  A  (12) 

which,  if  the  steam  is  used  at  100  pounds  gauge  (approximately  50  pounds  M.  E.  P.)  reduces  to  C  = 
227,  say  225  pounds  average  pressure  on  each  square  inch  of  projected  crank  pin.  This  figure  corres- 
ponds to  the  minimum  value  of  C  as  given  in  the  same  reference  and  is  considered  good  working  con- 
ditions for  high  speed  stationary  work.  It  should  be  noticed  however,  that  the  value  of  C  for  low 
speed  engines  and  for  locomotive  work  would  be  much  larger. 

After  obtaining  d  I  from  the  above  equation,  /  may  be  substituted  from  one  of  the  following  equa- 
tions to  find  d. 

Whitham  :  —  /  =    ---  --j—-       -   Allowing  .05  as  a  coefficient  of  friction. 

L-4 

• 

Marks  :  —          /  =  -       T  '  Allowing  .05  as  a  coefficient  of  friction. 

•h 

«.  .06  H.  P. 

Thurston  :  —  I  = 


Unwin:—    /     = 


J-t 

'3  H' 


where  L  =  length  of  stroke  in  feet,  and  r  =  radius  of  crank  in  inches. 

The  following  formula  is  suggested  as  giving  probably  the  best  results.    If  L'  =  stroke  in  inches 

(13) 

i. 26s  P  D  }      where  P  =  gauge  pressure. 
(M.  A.)       d  =  - 

N  (_  D  --  diameter  of  cylinder  in  inches. 

d    =  diameter  of  pin  in  inches. 

(M.  A.)       /  =  .0032  d  N)  N  =  R.  P.  M. 

These  formulas  may  be  used  for  checking. 

lo 


It  is  not  an  uncommon  practice  in  some  work  of  this  class  to  make  the  diameter  of  the  pin  equal 
the  diameter  of  the  shaft. 

Wrist  Pin: — The  projected  area  of  the  wrist  pin  (Trans.  A.  S.  M.  E.)  was  found  to  be,  from 
the  mean  pressure  exerted, 

d  I  =  .105  A  (14) 


Combining  this  with 


dl  = 


P  A 
C 


gives            C  =  476,  say  475  pounds  average  pressure  per  square 
inch  of  projected  area. 

Obtain  d  I  as  before  and  assume  either  d  or  I.  It  is  common  to  take  /  for  the  wrist  pin  about  one 

inch  less  than  that  of  the  crank  pin ;  or  a  value  for  the  diameter  may  be  obtained  from 


d  =    (.9  to  i)  / 
(M.  A.) :— d  =  .00325  P  D.  r.where  P 

1  D 

(M.  A.)  :— /  =  1.0495     d    I  d 


=  gauge  pressure. 
=  diameter  of  cylinder  in  inches. 
=  diameter  of  pin  in  inches. 


Cranks: — Side  cranks  are  usually  built  up  as  shown  by  Fig.  5.     The  cast  iron  disc  should  be 
fitted  to  the  shaft  by  a  pressed  fit.     Some  forms  of  crank  pins  are  also  fitted  in  this  way. 

Allowance  for  a  pressed  fit  can  be  taken  at 

.0025"  per  inch  of  diameter  of  shaft. 
For   reference   on   forced   fits   see : — American 
Machinist:  Feb.  16,  '99;  May  n,  '99;  Aug.  10,  '99. 
For  calculations  of  the  simple  side  crank  see 
formulas  under  center  cranks. 

Center  Cranks  are  usually  of  the  solid  forged 
type  as  shown  in  Fig.  6. 


FIG.  5. 

To  determine  the  section  E.  F.  put  the  engine  on  the  head  end  dead  center  and  assume  ioo#[]" 

on  the  piston  as  the  greatest  unbalanced  load  likely 
to  be  used.  Then  N  =  P  A  =  (too  A)  =  force 
acting.  The  unit  compressional  stress  on  E  F  due 
to  N  is 


N 

r 


MH 


fc   — 


PA 


2  a'  b 

The  unit  bending  stress  due  to  N  is 
P  A  M 


FIG.  7. 


Then  the  total  unit  stress  due  to  N  is 


(15) 


For  a  single  overhung  crank  (15)  becomes 


+  ^-)  O6) 

Since  there  are  here  two  unknowns,  a'  and  b,  it    will  be  necessary  to  assume  one  to  obtain  the  other. 

D 

Let  b  = 1-  i"  where  D  =  diameter  of  shaft  or,  (M.  A.)  : — b  =  .45  D  +  .5".     Substitute  b  in 

2 

equation  ( I )  and  find  a'. 

In  side  crank  engines,  the  crank  disc  is  usually  of  cast  iron,  and  consequently  in  applying  (16), 
b  is  made  proportionally  greater  than  for  center  crank  engines. 

To  determine  sec.  C.  D.  put  the  engine  so  that  the  crank  and  connecting  rod  are  at  right  angles, 
Fig.  8  and  assume  that  steam  follows  the  piston  for  half  stroke. 


M 


FIG.  8. 

We  then  have  a  combined  bending  moment  Tr  and  a  twisting  moment  Tin  which  according  to  Un- 
win,  Part  I  Paragraphs  44  and  126,  give  an  equivalent  bending  moment  of  approximately 

0.41  Tm 
M'  =  (0.91   Tr  +  -) 


The  bending  is  parallel  to  the  plane  of  rotation  hence  the  resistance  of  the  section  is  cr  b  ^-f-  6  and 
the  formula  for  dimension  of  section  becomes 


6  T 


(0.91r  +  0.205  m) 


This  formula  becomes  for  single  or  overhung  cranks. 


(17) 


(18) 


«=.         (0.91r  +  0.41w) 

The  rotative  effect  T  on  the  crank  pin,  of  the  horizontal  pressure  at  the  crosshead,  is 

("1.03  where  r  -f-  /  =  l/4 
T  =  P  A  1  1.02  where  r  -5-  /  =  # 

ti.oi  where  r  -=-  /  =  % 

The  value  of  /  should  be  between  1500  for  small  engines  and  2500  for  large  engines. 
Substitute  T,  f,  r,  and  m  and  find  a.    Check  this  with  (M.  A.)  :  —     a  =  1.185  D  where  D  =  di- 
ameter of  shaft. 

Counter  Balance:  —  In  designing  the  crank  we  are  confronted  with  the  problem  of  providing  a 
counter-balance  for  both  the  revolving  and  the  reciprocating  parts.    This  is  a  problem,  the  solution  of 

12 


which,  at  best,  can  be  but  a  compromise.     It  is  an   easy   matter  to  balance  the  rotating  parts  but  a 
complete  balance  for  the  reciprocating  parts  can  not  be  made.     (See  St.  Eng.  and  Boiler  Notes.) 

One  of  the  most  satisfactory  rules  for  counter-balancing  horizontal  engines  is  given  by  Unwin 


to  a 

where  M/1  =  weight   of   counter-balance   in    pounds. 
p     =  radius  of  center  cf  gravity  of  W± 

W2  --  weight  of  crank  pin  and  l/>  connecting  rod  in  pounds. 
Ws  ==  weight  of  reciprocating  parts  in  pounds. 
r     =  radius  of  crank  in  inches. 

Main  Bearing:  —  No  very  close  figures  can  be  given  on  the  length  of  the  main  bearing.    A  rough 
estimate  would  be,  say,  two  to  three  times  the  shaft  diameter.    A  more  satisfactory  figure,  however,  may 
be  obtained  from  Barr.     (Trans.  A.  S.  M.  E.)-    Let  d  I  =  projected  area  of  bearing,  then  d  /  =  C  A 
C  =  constant  varying  between  .367  and  .739 
A  -  -  area  of  piston  in  square  inches. 
Taking  the  mean  value  of  C  as  .489  the  formula  becomes 

d  /  =:  .489  A 

With  the  mean  value  of  C  and  a  steam  pressure  of  100  pounds  gauge,  the  average  pressure  per  square 
inch  of  projected  area  of  the  bearing  becomes  approximately  100  pounds.  If  the  minimum  and  max- 
imum values  of  C  were  used,  the  corresponding  pressures  would  approximate  140  and  70  pounds  respec- 
tively. 

The  average  size  taken  from  a  number  of  side  crank  engines  seems  to  show 

dl=   .7  A 

while  for  center  crank  engines  with  two  bearings  of  equal  size  the  value  approximates 

dl=  -55  A 

from  which,  knowing  the  shaft  diameter,  the  length  of  the  bearing  can  be  obtained. 

Connecting  Rod:  —  In  designing  the  connecting  rod  it  should  be  considered,  first,  as  a  rod  in  direct 
tension  and  compression,  in  which  case  a  fibre  stress  of  not  more  than  3000  pounds  per  square  inch 
should  be  used.  It  should  then  be  treated  as  a  long  column  which  can  buckle  in  two  ways  ;  first,  in  the 
plane  in  which  it  moves,  in  which  case  it  is  pin  ended  ;  second,  in  the  plane  perpendicular  to  the  plane 
in  which  it  moves  in  which  case  it  may  be  regarded  as  flat  ended.  Apply  Rankine's  or  Euler's  formula 
for  columns  and  determine  if  the  calculated  section  is  safe.  The  first  formula  will  more  satisfactorily 
apply  in  this  case.  See  Church  Par.  307. 

Ratio  of  breadth  to  height  of  rod  section.  —  In  Euler's  formula  P  =  force  which  will  produce  in- 
cipient flexure,  /'  and  J"  are  moments  of  inertia  of  the  sections  ;  then  considering  a  rectangular  sec- 
tion, if  b  ==  breadth  and  h  =  the  height  of  the  section,  /'  :  fa  b  h3  and  /"  =  fa  b*  h.  If  we  make 
the  rod  equally  strong  in  both  directions  we  have  P'  =  P"  or 


then  fa  b  h''  =  l/z  b3  h  or  h  =  2  b.  Hence,  we  learn  that  the  breadth  should  be  one-half  the  height 
of  the  section  to  be  uniformly  strong  in  each  plane.  The  above  is  based  on  the  assumption  that  the 
column  is  uniform  throughout  and  that  the  centrifugal  force  has  no  effect  on  the  rod.  As  a  matter 
of  fact,  in  practice  the  section  varies  ;  being  smallest  at  the  wrist  pin.  The  rod  is  also  subjected  to  a 
whipping  action,  such  that,  on  a  high  speed  engine  this  factor  has  considerable  effect.  No  very  def- 
inite information  on  this  point  can  be  obtained,  but  it  can  be  proven  that  with  a  rod  of  uniform  section 
throughout,  the  greatest  strain  comes  at  a  point  about  .6  the  length  of  the  rod  from  the  wrist  pin.  See 
following  problem. 

Because  of  the  fact  that  connecting  rods  are  subjected  to  such  severe  and  uncertain  forces,  manu- 
facturers make  the  height  of  the  sections  h  —  (2b  to  36)  the  average  value  being  h  =  2.5^.  It  will 
also  be  noticed  that  rectangular  rods  increase  in  section  as  they  approach  the  crank  pin.  The  amount  of 
taper  is  probably  more  a  factor  of  neatness  in  design  than  of  required  strength.  The  rod  should  be 
figured  for  strength  and  rigidity  and  use  this  section  next  to  the  wrist  pin,  whatever  excess  is  then 
added  for  taper  will  simply  increase  the  factor  of  safety. 

Kent  gives  as  the  distance  between  the  parallel  sides  of  a  rectangular  rod 

T  =  .01  D   VP  +  .6" 
where  D  =  diameter  of  cylinder  in  inches  and  P  •=  max.  unbalanced  pressure  in  pounds  per  square  inch. 

13 


Rods  having  rectangular  section  are  generally  used  on  high  speed  engines.  If  reference  to  sizes 
of  rods  having  other  shaped  sections  is  desired,  look  up  Kent,  page  799. 

The  following  sections  are  used  on  connecting  rods. 

A.  Slow  speed.     Corliss  Type.     Large  at  cen 

ter,  smaller  at  each  end. 

B.  Elliptical.     Used  on  straight  line  engines. 

C.  High   Speed  Engine  Type. 
AS)                 C                D              E.                   D.     High  Speed  Engine  Type. 

FIG.  9.  E.     Locomotive  Type. 

For  shapes  and  sizes  of  rod  ends  and  brasses  see  Unwin,  Vol.  11,  Pages  108-120;  Low  &  Bevis, 
pages  205-212;  "The  Constructor,"  pages  112-113;  Whitham,  pages  217-227;  Marks,  pages  53-61; 
Kent,  page  800. 

Greatest  Bending  Moment  in  the  Connecting  Rod: — Problem — Find  the  point  in  the  connecting 
rod  Fig.  10,  that  is  subject  to  the  greatest  bending  moment,  w  i>~  -=-  g  r  =  Centrifugal  load  at  the 
pin  where  K'  =  weight  in  pounds  per  unit  of  length.  With  the  load  at  the  cross  head  =  zero,  we  have  the 
conditions  shown  in  Fig.  ii/i.  e.,  a  beam  A  B  sustaining  a  load  varying  uniformly  from  w  v2  -f-  g  r 
to  o.  Assume  a  section  at  a  b,  a  distance  x  from 
the  supports,  and  we  have  .  \y  \i_ 

*  <*r 


FIG.   10. 


FIG.  ii. 


J      gr    I 

also     j?,  / 

ro    ty  V*~     1  —  X           , 
if  fi 

J      Z  r         I 

l 

h-M 
~i  —  i  —  —  ^. 

T-     —  '  —  - 

^s 

1 

^^^ 

k 

> 

> 

A                                 9* 

r 

wv*%                   wvM 

&cjr\                      t»5p 

FIG.  12. 

gr  3/ 


Tgrl 


IV  ' 


RI  = 

p 


w 


0  g  r 


r> 

.-.  /c,  = 


W  V2  I 


To  find  the  greatest  bending  moment,  consider 
the  section  .r  as  free,  and  Fig.  12. 


M  = 


6  gr 


•w  v-  x* 
"6  sr  I 


.  •  .  2  P  =  6  x2 

I 


V3 


=  .61 


Another  way  to  find  the  greatest  bending  moment  is  to  equate  the  shear  to  zero. 

W  V2  I         W  V2 


_ 

6  g  r       2  g  r  I  6 


2/' 


2  r-  —  6  x* 


Cress  Head: — The  maximum  pressure  on  the  cross  head  will  be,  with  cut-off  at  half  stroke,  W 
=  P  A  tan  3>  where  P  =  maximum  unbalanced 
pressure  on  piston  in  pounds  per  square  inch ;  but 
tan  $  =  r  -=-  /  and  W  —  P  A  (r  -5-  I).  Also,  W 
=  w  B,  where  w  =  pressure  in  pounds  per  square 
inch  of  bearing  surface  and  B  =  projected  surface 
of  one  side  of  the  cross  head  in  square  inches,  then 


w  B  =  P  A 


FIG.  13. 


The  value  of  w  is  taken  as  follows:  Rankine,  72.2;  Whitham,  100;  "The  Constructor,  60  to  120; 
Thurston,  66  to  100.  . 

There  seems  to  be  a  wide  diversity  of  practice  in  fixing  the  values  of  w,  some  builders  requiring 
a  value  as  low  as  30  while  others  will  permit  as  much  as  ten  times  that  amount.  It  is  desirable  in  high 
speed  engine  work  to  have  large  surfaces  and  low  pressures.  If  w  =  30,  P  =  100,  and  r  -=-  /  =  6, 
then  B  --  .55  A. 

For  mean  values  Barr  gives  B  --  .63  A  for  high  speed  engines,  and  .46  A  for  low  speed  engines. 

(M.  A.)  B  =  .75  H.  P. 

It  may  not  be  possible  on  account  of  some  feature  of  the  design  to  keep  to  these  figures,  but  the 
object  should  be,  to  assume  B  such  that  u>  will  be  between  30  and  75  pounds  per  square  inch. 

For  cylindrical  cross  heads,  the  diameter  may  be  taken  one  inch  larger  than  the  diameter  of  the 
cylinder. 

The  length  of  the  average  cross  head  is  /  "=   .9  L  where  L  =  length  of  stroke  in  inches. 
For  .details  of  cross  heads,  look  up  : — 

Unwin    , Vol.  II,  pages   121-136 

Low  &  Bevis    pages  218-228 

"The  Constructor" Pages   1 18-121 

Whitham    pages  208-216 

Marks    pages     44-  53 

Kent   page     798 

Piston  Rod: — The  piston  rod  may  be  regarded  first  as  a  piece  in  direct  tension  and  compression,  in 
which  case  the  allowable  stress  would  be  3,000  to  5,000  pounds  per  square  inch,  calculated  at  the 
weakest  section.  Again,  it  should  be  considered  as  a  long  column  under  compression,  and  by  the  use  of 
Euler's  or  Rankine's  formula  for  pin  and  square  ends,  determine  if  there  is  any  danger  of  buckling 
when  under  compression.  The  length  of  the  unsupported  part  of  the  rod  is  about  1.25  L. 

The  following  formulas  may  be  found  useful  in  determining  the  diameter  of  the  rod. 

\  d  =  .11 
U  = 


Barr  :— 


V  D  L  for  high  speed  engines. 

•  145  V~ 


L  for  low  speed  engines. 


Kent:—  d  —  .013  V  DLP 

Whitham: —        d  =  K  D     where  K  =  .16  for  steel. 


Seaton  :  — 

Marks  :  — 
Unwin  :  — 

Thurston  :- 




d  =     -p  V  P  where  F  =  45  to  50. 


d  =  .03525  V    D2  ^  p 
d  =  .0144  D    V~P 


d  = 


-f-  .0125  D. 


'where  a  =  10000  for  H.  S.  Engines. 
a  =  15000  for  L.  S.  Engines, 
and  L  =  length  of  stroke  in  ft 


Low  &  Bevis  :-d  =  .018  D  V  P 
(M.  A.)  :—         d  =  .018  D  V? 

In  all  the  above  the  following  notation  prevails,  except  where  otherwise  stated, 

15 


L  =  length  of  stroke  in  inches. 
D  =  diameter  of  cylinder  in  inches. 

P  =  maximum  unbalanced  pressure  in  pounds  per  square  inch. 
Piston  Face: — The  piston  face  varies  from  .2  D  to  .5  D. 


Marks: —  Piston  face  1=   V    L  D. 

Barr:-  Piston  face  1=     H6  ^  Jor  f^  sPee,d  en?mes' 

I  .32  D  for  low  speed  engines. 

I.  C.  S.:—  Piston  face  I  —  .2  D  +  1.5" 

(M.  A.)  :— Piston  face  /  =  .43  D. 

In  all  the  above,  L  =  length  of  cylinder  in  inches  and  D  =  diameter  of  cylinder  in  inches. 

For  shapes  of  piston  details,  see 

Whitham    ....'. Pages      1 1-  25 

Unwin Vol.  II,  Pages  136-159 

Low  &  Bevis   Pages  229-238 

Holmes  Pages  208-213 

Packing1  Rings: — Packing  rings  are  turned  about  j3e -",  to  each  foot  of  diameter,  larger  than  the 
cylinder,  and  a  portion  is  then  cut  out  of  them  so  the  ends  just  come  together  when  fitted  for  use.  A 
good  thickness  for  rings  is 

t  =  .03  D 

(M.  A.)  :  —  t  =     .8  iv     where  w  =  width  of  ring  in  inches. 
The  width  of  rings  varies  a  great  deal  according  to  various  authorities. 

Unwin  w  =  .014  D   +  .08". 

Whitham  w  =  .15  D 

In  the  two  formulas  the  width  of  the  ring  would  vary  in  a  10"  cylinder  by  a  factor  of  7.  In 
practice,  the  piston  ring  varies  from  a  width  of  fy$"  in  the  smaller  sizes  to  %"  in  the  larger  sizes. 

(M.  A.)  :—  w  —  .055  D. 

Cylinder  Walls: — It  will  be  found,  in  figuring  the  cylinder  walls  to  resist  the  internal  pressure, 
that  even  if  we  allow  a  large  factor  of  safety,  the  calculated  sizes  run  much  below  the  sizes  commonly 
used  in  practice.  The  cylinder  is  designed  heavy  for  other  reasons,  chiefly  for  rigidity  and  for  re- 
boring.  Piobably  the  most  commonly  used  formula  for  the  cylinder  thickness  is 

Barr :—  t  =  .05  D  +  .3" 

where  D  —  diameter  of  cylinder  in  inches. 

t  =  thickness   of  walls  in  inches. 

This  formula  agrees  with  practice  in  smaller  sized  engines  but  gives  results  below  practice  in  the 
larger  engines.  The  following  may  be  considered  very  close  to  the  average. 

(M.  A.)  :—  t  —  .07  D  +  .125" 

The  above  formulas  apply  to  a  steam  pressure  of  100  pounds.  If  the  steam  pressure  is  increased 
the  constant  should  also  be  increased. 

Cylinder  Flanges: — The  thickness  of  the  cylinder  flange  is  usually  taken  at  a  certain  per  cent  of 
the  cylinder  thickness. 

Barr:—  f  =  1.25  t 
where  t  =  cylinder  wall  thickness. 

(M.  A.)  :—  t'  =  .12  D. 

where  D  =  diameter  of  cylinder  in  inches. 

Cylinder  Head: — The  cylinder  head  will  be  from  i  to  1.5  times  the  thickness  of  the  cylinder.  It 
should  fit  to  the  cylinder  metal  to  metal.  Ordinarily  there  will  be  two  cylinder  htads  considered; 

16 


head  end,  and  crank  end.     The  crank  end  head  forms  the  dividing  line  between  the  bed  and  the  cylin- 
der.    There  are  four  methods  of  construction  here. 

(1)  Bed  and  cylinder  cast  solid,  used  only  on  very  small  engines. 

(2)  Cylinder    head    separate    and   bolted    between  the  cylinder  and  bed. 

(3)  Cylinder  head  part  of  the  cylinder. 

(4)  Cylinder  head  part  of  the  bed. 

Cylinder  Head  Studs:  —  The  number  of  studs  may  be  taken 

N  =  0.7  D 

Always  use  an  even  number  of  studs.  The  diameter  is  usually  not  less  than  Jxs"  and  varies  from 
this  to  say  i^".  The  diameter  should  be  figured  from  the  tension  on  the  area  at  the  root  of  the 
thread.  This  may  be  then  compared  with 

Barr:—  d  =  .025  D  +  .5" 

Counter  Bore:  —  The  counter  bores  should  be  such  that  the  packing  rings  will  pass  the  entire 
length  of  the  cylinder.  Allowance  of  %"  to  YZ"  in  diameter  is  made.  The  counter  bore  should  curve 
down  to  meet  the  cylinder  proper. 

All  drips  are  tapped  into  the  counter  bore. 

Steam  Pipe:  —  The  velocity  of  the  steam  for  engine  service  will  vary  from  5000  to  6000  say  5500 
F  P  M.  A  rational  formula  for  the  amount  of  steam  passing  through  a  pipe  is 


.  .       , 

where  Q  =  volume  of  steam  in  cubic  feet.  C  =  velocity  in  F.  P.  M.  a  =  area  of  pipe  in  square  inches. 
The  formula  for  the  steam  engine  cylinder  is 

2  =  --  <20) 


where  A  =  area  of  piston  in  square  inches,  and  V     -  velocity  of  piston  in  F.  P.  M. 

Co,         AV          AV 

Equating  we  have  -    or   —^  —    =  a 

144  144  C 

Now,  if  V  =  600  and  C  =  5500  then,  a  =  .11  A.  Check  this  with 


Kert :—  d  =  .408  V  H.  P. 

Exhaust  Pipe: — Low  pressure  steam  will  not  flow  as  fast  as  high  pressure  steam,  hence,  C  should 
be  taken  less,  (2500  to  5000,  Barr),  say  3800  then  as  above 

o  =  .16  A 
Kent: —  a  =   25  to  50  per  cent  greater  than  steam  pipe. 

Cylinder  Ports: — The  ports  or  passages,  through  which  the  steam  enters  the  cylinder,  should  be 
short,  direct,  of  easy  curvature  and  large  enough  to  prevent  wire  drawing  of  the  steam.  It  seems  to 
be  current  practice  to  figure  the  area  of  the  port  from  a  steam  velocity  of  from  5000  to  55°°  F.  P.  M. 
Assuming  the  lower  figure  for  ports  that  handle  both  live  and  exhaust  steam,  we  have 

a  =   .12  A. 

Other  formulas  for  area  of  ports. 

Hubbard  a  =  .1  A 

I.  C.  S.  a  =  .11  A 

(M.  A.)  a  =  .113  A 

The  length  of  the  port  varies  from  .7  D  to  D. 

I.  C.  S.  /  =  .70 

Hubbard  /  =  .75  D 

(M.  A.)  /  =  .95  D 

Recent  practice  is  making  the  length  of  the  port  about  equal  to  the  diameter  of  the  cylinder. 
To  serve  as  a  check  in  working  up  the  Zeuner,  the  following  ratios  are  added.    These  must  not  be 
-onsidered  as  fixed  values,  they  merely  represent  the  average,  as  others  before  given. 
Valve  Travel   (Max.)  5  =  .269'!,. 
Steam  Lap  =  width  of  port. 


STEAM  BOILER  DESIGN. 
General. 

In  designing  a  steam  boiler  the  following  points  should  be  kept  in  mind. 

First,  the  boiler  should  have  a  good  circulation  of  the  water  and  should  steam  rapidly.  To  have 
a  good  circulation,  the  water  must  have  a  free  path  from  the  point  of  greatest  heat  to  all  points  within 
the  boiler  am1  this  path  must  not  be  seriously  obstructed  by  short  or  abrupt  turns.  To  be  a  good 
steaming  boiler  it  must  have  a  large  amount  of  heating  surface,  a  large  grate  area  and  a  water  space 
well  broken  up  into  small  volumes.  The  term  heating  surface  is  understood  to  refer  to  any  surface 
having  the  heated  gases  on  one  side  and  water  on  the  other.  No  surface  in  the  steam  space  should 
be  exposed  to  the  heated  gases. 

Second,  the  boiler  should  be  built  compactly  and  should  be  easily  accessible  for  cleaning  and  re- 
pairs. Floor  space  in  the  average  boiler  room  is  valuable  and  other  things  being  equal  the  boiler  re- 
quiring the  least  floor  space  will  be  first  considered  by  the  purchaser.  The  cleaning  of  a  boiler  is  also 
an  important  matter  in  power  house  work  and  the  designer  should  so  arrange  the  parts  of  the  boiler 
that  all  may  be  easily  reached. 

Third,  the  boiler  should  be  strong  enough  to  be  safe  under  its  rated  steam  pressure  and  should 
have  provision  for  the  expansion  and  contraction  of  its  parts  without  endangering  those  parts,  or  the 
boiler  setting  which  surrounds  them. 

There  are  two  general  classes  of  boilers,  fire  tube  and  water  tube.  The  fire  tube  boiler  is 
the  old  form  and  is  built  vertical  or  horizontal,  tubular  or  flue.  The  typical  representative  fire  tube 
boiler  is  the  horizontal  tubular  or  "Multitubular"'  boiler  as  it  is  called.  The  water  tube  boiler  is  of 
more  modern  design,  and  is  usually  built  in  sections.  Typical  forms  of  this  class  of  boilers  are  the  Bab- 
cock  and  Wilcox,  Sterling,  Wickes  and  Heine.  The  chief  features  which  distinguish  the  water  tube 
from  the  fire  tube  boiler  are,  first,  water  circulation  on  the  inside  of  the  tubes ;  second,  reduced  water 
space  and  its  subdivision  into  smaller  units;  third,  increased  heating  surface. 


PROBLEMS  IN  MULTITUBULAR  BOILER  DESIGN. 

Having  given  the  steam  consumption  of  the  engine  in  the  previous  design,  find  the  equivalent 
evaporation  of  the  boiler.  It  would  be  well  here  to  assume  a  steam  consumption  of  the  engine  about 
25  per  cent  greater  than  the  rated  amount..  The  boiler,  under  such  conditions,  would  then  supply 
enough  steam  to  allow  for  a  certain  overload  on  the  engine. 

To  obtain  this  equivalent  evaporation  take — ( Engine  horse  power)  X  (pounds  of  steam  per 
horse  power  hour)  X  (total  heat  in  steam  at  absolute  pressure — total  heat  in  water  entering  boiler 
at,  say,  212  degrees  F.)  divided  by  (34.5  X  965.6) 

PROBLEM  i.  Determine  the  following  dimensions  for  a  ....  H.  P.  boiler,  (a)  Heating  surface ; 
(b)  Grate  surface;  (c)  Diameter  and  length  of  tubes;  (d)  Heating  surface  in  tubes.  (  f 
of  the  total  H.  S.  approx.)  ;  (e)  Number  of  tubes;  (f)  Ratio  of  the  total  tube  area  to 
grate  area.  For  size  of  boiler  tube  area  see  Kent,  page  196;  (g)  Volume  of  the  shell, 
(water  space  +  steam  space  +  volume  of  tubes);  (h)  Diameter  of  the  boiler  shell; 
(i)  Height  of  water  line. 

PROBLEM  2.     Lay  out  the  tube  sheet.    This  should  be  done  experimentally  on  a  trial  sheet. 

PROBLEM  3.  After  completing  the  lay-out  of  the  tube  sheet,  check  the  calculations  in  Problem  I 
on  the  following  points :  heating  surface,  nominal  rate  of  evaporation,  ratio  of  the  tube 
openings  to  grate  area,  and  volume  of  shell. 

PROBLEM  4.     Determine  the  distance  E;  Fig.  14,  also  the  total  stack  area. 

18 


PROBLEM  5.     Find  the  area  above  the  tubes  in  the  tube  sheet  and  determine  the  total  load  on  the 

stays. 
PROBLEM  6.    Locate  the  boiler  stays. 


FIG.  14. 

PROBLEM   7.     Determine  the  size  and  the  spacing  of  the  rivets  to  prevent  the  failure  of  the  stay 

bolt  fastening. 

PROBLEM  8.     Determine  the  size  of  the  stay  bolt  body. 
PROBLEM  9.     Plan  the  longitudinal  seams  of  the  boiler  shell  and  calculate  the  efficiency  of  the 

same. 

PROBLEM   10.     Plan  the  girth  seams  and  calculate  the  efficiency  of  the  same. 
PROBLEM    n.     Calculate   the   factor   of   safety  in  the  entire  boiler  taking  into  account  the  strength 

of  the  joints. 

PROBLEM  12.     Determine  the  diameter  of  the  steam  pipe,  feed  pipe  and  blow-off  pipe. 
PROBLEM  13.     Estimate  the  total  weight  of  the  boiler. 
PROBLEM  14.     Estimate  the  weight  of  the  boiler,  when  working  under  normal  conditions. 

(a)  Weight  of  boiler  and  accessories,    ( .  . )   pounds. 

(b)  Weight  of  water  in  boiler    *  (.  .)   pounds. 

(c)  Weight  of  steam  in  boiler.  (. .)  pounds. 
Grand  Total,  ( . . )  pounds. 

PROBLEM    15.     Calculate  the  number  of  rivets  in  each  boiler  leg  or  support. 

PROBLEM  16.     Calculate  the  intensity  of  the  pressure  between  the  leg  and  the  boiler  setting. 


NOTES   ON   THE   DESIGN  OF  MULTITUBULAR  BOILERS. 

References: — The  designer  is  expected  to  consult  Hutton's  "Mechanical  Engineering  of  Power 
Plants,"  Peabody  and  Miller's  "Steam  Boilers,"  Whitham's  "Constructive  Steam  Engineering," 
"Kent,"  trad;  catalogues  and  the  like  and  become  familiar  with  the  general  shapes  in  the  design  of 
boiler  parts.  He  should  also  study  the  average  boiler  setting  and  note  the  methods  of  construction  in 
furnace,  grates,  bridge  wall,  flame  way,  rear  arch,  front  connections,  smoke  nozzle  and  breeching.  Two 
plates  of  drawings  accompany  these  notes.  They  represent  average  student  work  and  are  added  mere- 
ly to  illustrate  how  the  sheets  may  be  compiled.  It  is  requested  that  each  designer  make  a  report  con- 
taining the  theoretical  part  of  the  work  and  that  only  one  complete  set  of  plates  need  be  made  as  a 
part  of  the  engine  set.  These  tracings  may  be  retained  at  the  University  but  the  reports  will  be  re- 
turned at  graduation.  The  horse  power  of  the  boiler  to  be  designed  will  be  such  as  to  supply  steam 
to  the  engine  just  completed. 

Capacity  of  the  Boiler: — This  will  depend  upon  three  things;  grate  area,  heating  surface,  and 
steam  and  water  space.  Of  the  three,  the  heating  surface  is  of  prime  importance.  A  very  satisfac- 
tory definition  of  heating  surface  is  found  in  Kent,  page  679.  Heating  surface  =  :  %  area  of  shell  + 
area  of  tubes  +  %  area  both  heads  —  2  X  cross  sectional  aroa  of  all  tubes.  The  heating  surface  of 
tubes  should  be  measured  on  the  inside. 

Commercial  Boiler  Rating: — Boilers  are  usually  rated  in  the  term  horse  power.  They  are  de- 
signed on  the  basis  of  the  steam  consumption  of  the  engines  they  are  to  supply.  Boilers  are  installed 
however,  of  larger  capacity  than  that  indicated  by  the  commercial  engine  rating  because  of  the  usual 
under-rating  of  the  engines  and  because  it  is  desired  to  supply  ample  steam  without  forcing.  Twenty- 
five  per  cent  increase  would  represent  a  fair  average.  A  boiler  horse  power  is  stated  as  follows : 

Horse  Power: — One  boiler  horse  power  equals  30  pounds  ot  steam  evaporated  from  feed  water  at 
100°  F.  to  dry  steam  at  70  pounds  gauge  pressure,  or  34.5  pounds  of  water  evaporated  from  and  at 
212°  F. 


All  engines  do  not  require  the  same  amount  of  steam  per  horse  power.  The  following  values  may 
be  taken  for  high  speed  engine  practice.  Simple,  30  to  32  pounds  per  H.  P.  hour.  Compound  non- 
condensing,  24  to  26  pounds  per  H.  P.  hour.  Compound  condensing,  18  to  20  pounds  per  H.  P.  hour. 

Heating  Surface  and  Grate  Surface:— 

Heating  surface  per  Boiler  H.  P. 
Grate  surface  per  Boiler  H.  P. 
Ratio  of  H.  S.  to  G.  S. 
Water  evaporated  per  sq.  ft.  of  heat- 
ing surface  per  hour  from  and  at  212°  F. 

The  grate  surface  is  from  30  to  50  per  cent  air  space. 


"•5 
-33 

34-5 


square 
square 


feet, 
feet. 


3       pounds. 


Tubes: — The  tubes  must  be  of  sufficient  area  to  carry  away  the  products  of  combustion.  A 
good  proportion  is 

Area  of  tubes  :  Area  of  the  grate  =  i   :  8 

The  length  of  the  tubes  is  about  5  feet  for  each  one  inch  in  diameter.  Outside  diameter  of  tubes 
=  2",  2y2".  3",  31/2"  and  4".  In  general,  large  boilers  have  large  tubes  and  small  boilers  have 
small  tubes;  say  20  H.  P.  2";  60  H.  P.  2l/2" ;  100  H.  P.  3",  etc.  These  values  are  not  definitely  fixed 
but  are  a  fair  average.  From  |  to  f  of  all  the  heating  surface  is  in  the  tubes. 

Steam  Space : — Allow  .8  to  i  .o  cubic  foot  per  horse  power.  This  amounts  to  approximately  *4 
the  interior  volume  of  the  boiler. 

Length  of  the  Boiler: — The  length  of  the  boiler  proper  is  the  overall  length  at  the  tube  sheets. 
Having  found  this  the  designer  then  selects  between  flush  front  and  extended  front  as  shown  in  Figs. 
15  and  16.  The  length  x  of  the  smoke  box  can  be  taken  0.08  H.  P.  +  10".  The  Atlas  Engine  Company  of 
Indianapolis  makes  x  constant  for  all  sizes  =  15". 


I  Dome 


I  C 


FIG.  15. 


FIG.  16. 


Stack  Area  and  Area  Over  Bridge  Wall:— The  following  relation  holds  good  for  area  of  stack 
and  area  over  bridge  wall. 

Area  of  stack  :  Area  of  Grate  =1:9 

Area  over  bridge  wall  :  Area  of  Grate  =1:7 

Materials.     General : — The  materials  used  in  boiler  work  are : 

Shell;  Mild  Steel :  fire-box,  flange  and  open  hearth. 

Rivets  and  Braces;  wrought  iron  preferred. 

Fittings;  cast  iron,  malleable  iron  and  mild  steel. 

On  all  plates,  the  elastic  limit  should  be  at  least  one  half  the  ultimate  strength.  The  percentage  of 
manganese  and  carbon  are  left  to  the  judgment  of  the  steel  maker. 

Steel  up  to  l/2  inch  thickness  must  stand  bending  double  and  being  hammered  down  on  itself, 
above  that  thickness  it  must  bend  round  a  mandrel  having  a  diameter  of  il/2  times  the  thickness  of 
the  plate,  down  to  180°,  all  without  showing  signs  of  distress. 

Test  pieces  are  cut  both  lengthwise  and  crosswise  of  the  plate,  each  piece  to  have  a  length  not 
less  than  16  X  thickness  of  plate.  All  rough  sheared  edges  should  be  milled  or  filed  off. 


20 


Important  Qualities: — 


Shell  plates  not  exposed  to  direct  fire. 


f  Tensile  strength,  65000,  7oooo*l]" 
J  Elongation — Not  less  than  24%  in  8" 
I  Phosphorus — Not  over  .035% 
^Sulphur — Not  over  .035% 


fTensile  strength,  60000,  65000*°" 

Shell  plates  exposed  to  direct  fire,  or  plates  on   J  Elongation  not  less  than  27%  in  8" 
which  flanging  is  to  be  done.  1  Phosphorus  not  over  .03% 

I  Sulphur  not  over  .025% 

C Tensile  strength  55ooo-62OOoS[1" 
Fire  box  plates,  exposed  to  direct  fire  or  flanged    J  Elongation  30%  in  8" 

over  the  greater  portion  of  their  periphery.     |  Phosphorus  not  over  .03% 

I  Sulphur  not  over.  .025% 

Cast  Iron: — All  cast  iron  shall  have  a  soft,  gray  texture  and  a  high  degreee  of  ductility.  It  will 
be  used  only  on  crabs,  yokes,  hand  hole  plates,  man  heads,  etc.  It  should  not  be  used  on  mud  drums,  legs, 
necks,  headers,  manhole  rings  or  any  part  of  the  boiler  subjected  to  tensile  stress. 

Shell: — Boiler  shells  until  recently,  were  wrought  iron,  but  with  the  advent  of  high  steam  pres- 
sures, open  hearth,  or  crucible  steel  containing  about  J4  of  one  Per  cent  of  carbon  replaced  it.  The 
ultimate  strength  of  this  steel  is  55000  to  700008"".  Allowable  fiber  stress  about  8ooo*[1".  Steel  plate 
is  more  susceptible  to  injury  during  forming  than  wrought  iron  plate. 

The  number  of  riveted  seams  in  a  boiler  should  be  as  few  as  possible.  In  small  boilers  it  is  possible 
to  make  one  longitudinal  seam  suffice,  having  the  length  of  the  plate  running  lengthwise  with  the  boil- 
er. Fig.  1 7  A.  In  large  boilers  the  plates  become  too  large  to  be  cheaply  produced  and  two  or  more 
sheets  are  used  as  in  B.  Generally  however,  boilers  are  made  from  rings  as  in  Fig.  18. 


ooooooooooooooo 

)  O  O  O 

FIG.  17. 


STATIONARY 


LOCOMOTIVE. 


FIG.  18. 

When  a  sheet  is  selected,  it  is  marked  with  a  template  and  either  punched  or  drilled,  after  this  it 
is  rolled  to  the  desired  curvature  and  riveted.  The  holes  are  prepared  for  riveting  by  either  punching, 
which  is  the  cheapest  method,  punching  and  reaming,  or  drilling. 

Thickness  of  the  Shells — The  force  tending  to  burst  the  boiler  shell  longitudinally  is  P  D,  where 
P  =  gauge  pressure  in  pounds  and  D  —  diameter  of  shell  in  inches.  The  resisting  force  is  2  t  f,  hence 
the  thickness  of  plate  =  P  D  -f-  2  f.  Since  the  thickness  of  the  plate  to  resist  transverse  rupture  is 
only  half  as  great,  (t=  P  D  -i-  4  f)  the  first  formula  should  be  used  for  boiler  shells. 

21 


r 

a! 


•^ 

I 


° 

x 


P  D 

Kent  gives  t  =  -    -  where  /  =  ioooo#[1"  and  c  =   .70  for  a  double  riveted  longitudinal  seam. 
9fc 

The  following  data  shows  the  maximum  sizes   of  plates  that  may  be  ordered  from  the  rolling  mills. 
(1904). 

LARGE  MILL.— MAXIMUM  SIZES  OF  PLATES. 


Thick- 
ness of 
Plates 

144 

140 

135 

130 

125 

WIDTH  OF 
120   110 

PLATE  IN 
100 

INCHES 
90    80 

70   60   50    40 

30 

Diam. 
of  head 
that 
can  be 
rolled 

X" 

150 

180 

240   260 

280  300  340  360 

420 

124 

-iV 

220 

240   250 

260 

270   280 

300  340  360  390 

510 

140 

K; 

180 

200 

220 

240 

280   300 

340 

360   380 

400  420  480  520 

560 

144 

T^" 

180 

200 

220 

240 

300   340 

380 

420   440 

480  520  540  560 

too 

144 

>A' 

144 

200 

220 

240 

260 

300   340 

380 

420   440 

480  520  540  560 

600 

146 

A" 

144 

200 

220 

240 

260 

300   340 

380 

420   440 

480   520  540  560 

600 

146 

«' 

144 

200 

220 

240 

260 

30(1   340 

380 

420   440 

480  520  540  560 

600 

146 

H" 

144 

200 

220 

240 

260 

300   340 

380 

420   440 

480  520  540  560 

600 

146 

X? 

144 

200 

220 

240 

26i) 

300   340 

380 

400   440 

480  520  540  560 

600 

146 

ff' 

144 

200 

220 

240 

260 

300   340 

380 

400   420 

460  480  500  540 

580 

146 

W 

144 

200 

220 

240 

260 

300   340 

380 

400   420 

460  480  500  540 

580 

146 

\i" 

200 

220 

240 

260 

300   340 

380 

400   420 

460  480  500  540 

5oO 

146 

1  • 

180 

220 

240 

260 

300   340 

380 

400   420 

460  480  500  540 

560 

146 

l#' 

180 

210 

240 

260 

280   320 

360 

380   400 

440  460  480  500 

540 

144 

IX" 

180 

210 

240 

260 

280   320 

360 

380   400 

440  460  480  500 

540 

144 

1^8" 

180 

210 

220 

240 

260   300 

340 

360  380 

420  440  460  480 

500 

144 

!#• 

160 

200 

220 

240 

260   300 

340 

360   380 

420  440  460  480 

500 

144 

IX' 

160 

200 

210 

220 

240   260 

300 

320   340 

380  400  400  420 

480 

142 

IK" 

150 

190 

200 

210 

220   240 

260 

280   320 

360  380  380  400 

460 

142 

2  ' 

140 

170 

180 

190 

200   220 

240 

260   300 

340  360  360  380 

440 

142 

LENGTH  OF 

PLATE  IN 

INCHES 

Rivets: — All  rivets  shall  be  good  charcoal  iron  or  soft  mild  steel,  having  the  same  properties  as 
fire  box  plates.  They  must  test  hot  and  cold  by  drawing  down  on  an  anvil  with  the  head  in  a  die. 
They  must  also  test  by  nicking  and  bending  and  by  bending  back  on  themselves  cold,  all  without  devel- 
oping cracks  or  flaws. 

The  tensional  fibre  stress  of  all  wrought  iron  rivets  should  not  be  taken  at  more  than  6000  pounds 
per  square  inch.  The  general  forms  of  rivet  heads  are  shown  in  Fig.  21. 


\ 


D 


PIG.  21. 


A Conical  head,  usually  hand  work. 

B Cup  head,   swage  and  snap  die  work. 

C Rounded  head,  machine  work. 

D Countersunk. 

Approximate  values  of  riveted  joints: — 

The  Diameter  of  rivets  for  different  thickness  of  plate  according  to  Unwin,  Part  I,  page  103,  is, 
if  t  =  thickness  of  plate  in  inches 

d  =  1.2   y  t 

The  Pitch  of  the  rivet  (minimum)  is,  p  =  2  d.     The  distance  from  the  center  of  the  rivet  to  the 
edge  of  the  plate  is,  a  =  1.5  d  -f-  1-16  inches. 

24 


Tube  Sheet: — The  thickness  of  the  tube  sheet  is  generally  -fe  to  £  inch  thicker  than  the  shell. 
The  holes  for  the  tubes  should  be  punched  %  inch  less  than  the  required  diameter  and  reamed  to  full 
size,  or  drilled,  and  slightly  countersunk  on  both  sides.  The  hole  should  finish  B'T  to  ^  inch  larger 
than  the  diameter  of  the  tube,  for  small  and  large  tubes  respectively.  Where  copper  ferrules  are 
used  the  hole  should  be  a  neat  fit  for  the  ferrule.  Xos.  18  to  14  wire  gauge  copper  should  be  used  in 
fire  tube  boilers  on  ends  subjected  to  the  direct  heat. 
The  tube  sheet  should  be  annealed  after  punching 
and  before  reaming. 

Tube  ends  in  the  furnace  are  beaded  to  the 
tube  sheet ;  those  in  the  smoke  box  are  usually  rolled 
to  fit  and  allowed  to  project  }4  to  JH$  inch  beyond 
the  tube  sheet. 

Bracing  the  Tube  Sheet: — The  tubes  are  sup- 
posed to  give  sufficient  rigidity  to  that  part  of  the 
boiler  head  filled  by  them ;  the  upper  segment,  how- 
ever, and  occasionally  the  extreme  lower  part  sur- 
rounding the  manhole  or  handhole,  needs  staying. 
Boiler  stays  are  of  four  kinds;  through  stays,  which 
are  the  simplest  and  most  effective  and  are  used 
where  heavy  forces  are  to  be  resisted,  especially  near 
the  central  part  of  the  boiler  ;  angle  stays,  used  where 
medium  lengths  are  desired ;  gusset  stays,  for 
the  short  bracing  between  the  head  and  the  shell ; 
and  the  girder  stay  or  crown  bar,  which  is  used 
generally  to  strengthen  the  crown  sheet  and  upper 
plates  around  the  fire  box. 

The  stay  bol'  is  a  form  of  through  stay  which 
is  used  to  support  the  flat  sides  around  the  fire  box. 
Fig.  22.  shows  some  of  the  methods  of  fastening  the 
various  forms. 

To  find  the  area  to  be  stayed,  let  the  shell  sup  port  from  2  to  3  inches  and  the  tubes  from  i  to  2 
inches  above  the  upper  line  of  the  tubes,  Fig.  23.  Find  the  remaining  area  of  the  segment  and,  if 
p  is  the  unbalanced  pressure  on  the  head  in  pounds  per  square  inch,  the  total  load  to  be  stayed  will  be 
p  A.  Next  find  the  number  of  stays  to  be  used.  The  following  formula  is  given  for  use  in  spacing 
the  stavs. 


FIG.  22. 


a  =  t  "V 


9f~ 
ap 


a  =  distance  between  stays  in  inches. 

t  =  thickness  of  head  in  inches. 

f  =  Working  fibre  stress  of  the  metal  6000 

for  wrought  iron  and  8000  for  special  steel. 

p  =  boiler  pressure  in  pounds  per  square  in. 
Take  this  value  as  the  approximate  distance 
between  stay  centers,  and  from  the  load  on  each 
stay  calculate  its  size  of  cross  section.    Calculate  al- 
so for  a  safe  fastening  to  the  shell  or  head. 

The  load  on  the  head  is  perpendicular  to  the 
tube  sheet  consequently  the  actual  load  on  any  angle 
stay  will  be,  Fig.  24. 


S  = 


FIG.  23. 
load  to  be  stayed 


or 


cos  0 


Area  of  angle  stay  = 


area  of  through  stay 

COS0 


FIG.  24. 


The  angle  6  which  an  angle  brace  makes  with  the  shell  should  never  exceed  30  degrees,  it  is  pre- 
ferred that  the  angle  be  about  18  or  20  degrees. 

Where  through  stays  are  used  they  should  be  spaced  so  they  will  not  cut  off  entrance  to  the  boiler 
from  above. 

The  material  used  in  stays  should  be  iron  or  mild  steel  especially  manufactured  for  the  purpose 
and  must  show : 

fTensile  strength  not  less  than  46ooo#[1" 
I  Elongation  not  less  than  22%  for  bolts  less  than  in"  area 
]  Elongation  not  less  than  20%  for  bolts  more  than  i[1"  area 
[^Elastic  limit  not  less  than  26000  t°" 

fTensile  strength  not  less  than  55OOO#n" 
I  Elongation  not  less  than  25%  for  bolts  less  than  i[I"  area 
\    Elongation  not  less  than  22%  for  bolts  more  than  i[1"  area 
I  Elastic  limit  not  less  than  33000  8[1" 

Tests  : — A  bar  taken  at  random  from  a  lot  of  1000  pounds  or  less,  threaded  with  a  sharp  die  "V" 
thread  with  round  edges,  must  bend  cold  180  degrees  around  a  bar  of  same  diameter  without  showing 
any  crack  or  flaw. 

Boiler  Tubes: — All  tubes  shall  be  charcoal  Iron  or  Mild  Steel  specially  made  for  the  purpose, 
lap  welded  and  drawn.  They  must  be  round,  straight,  free  from  scales,  blisters  and  mechanical  de- 
fects, and  each  tested  to  500  pounds  per  square  inch  inter  hydrostatic  pressure. 

Mechanical  Test. — A  section  from  one  tube  taken  at  random  from  a  lot  of  150  or  less,  must 
stand  hammering  down  cold  vertically  without  cracking  or  splitting  when  down  solid. 

Length  of  test  pieces. 

y$"  for  tubes  from  i"  to  i%"  diam. 
i"  for  tubes  from  2"  to  2j^"  diam. 
i>4"  for  tubes  from  2%"  to  3>4"  diam. 
il/2"  for  tubes  from  35/2"  to  4"  diam. 
1^4"  for  tubes  from  4^/2"  to  5"  diam. 

In  arranging  the  tubes  in  the  tube  sheet  of  the  average  boiler  locate  the  upper  line  of  tubes 
so  there  will  be  approximately  6  inches  between  the  normal  water  line  and  the  top  of  the  tubes. 
Stationary  boilers  usually  have  the  tubes  in  vertical  and  horizontal  rows  with  a  large  space  down 
the  center  to  aid  circulation.  Allow  from  ^4  inch  to  i  ^  inch  between  vertical  rows  and  from  l/2 
inch  to  %  inch  between  horizontal  rows.  Locomotive  boiler  tubes  are  staggered  on  30  degree  lines. 
This  gives  a  possibility  of  putting  in  a  greater  number  of  tubes  than  if  they  were  in  vertical  and 
horizontal  rows.  Tubes  should  not  come  within  2  or  3  inches  of  the  shell.  Allow  room  for  hand 
holes  and  manholes  in  the  upper  or  lower  part  of  the  head  for  cleaning.  A  manhole  is  preferred. 

Manholes  and  Handholes: — For  shapes  and  sizes  of  openings  and  plates  to  fit  them  see  "Ryer- 
son's  Monthly  Journal  and  Stock  List."  See  also  shapes  and  sizes  of  crabs-. 

Dome  and  Dry  Pipes : — There  seems  to  be  no  rational  basis  for  determining  the  sizes  of  the 
steam  dome.  The  diameters  vary  from  24"  for  a  40  H.  P.  boiler  to  32"  for  a  100  H.  P.  boiler. 
The  height  of  the  dome  is  usually  made  equal  to  the  diameter.  Note  the  style  of  construction  in 
Hutton,  Figs.  362,  365  and  369.  The  latter  is  recommended  by  the  H.  S.  B.  &  I.  Co.  When  a  dome 
is  used  it  need  not  be  stayed  if  the  top  is  curved  to  a  radius  equal  to  or  Jess  than  the  diameter  of  the 
dome.  A  flat  topped  dome  should  be  stayed. 

Domes  are  used  on  locomotive  and  portable  boilers,  but  are  not  especially  to  be  recommended 
on  stationary  boilers.  The  dry-pipe  is  preferred  by  many  to  the  dome  because  it  weakens  the  boiler 
less  and  permits  more  compactness  in  design.  A  typical  dry-pipe  is  shown  in  Fig.  25.  The  top 
of  each  leg  L,  L'  is  drilled  with  J4"  holes  such  that  the  combined  area  of  the  holes  is  equal  to  or 
greater  than  the  area  of  the  delivery  pipe.  One  row  of  larger  holes  ($/&"  to  y2")  spaced  5  or  6  inch 
centers  is  drilled  through  the  under  side  to  drain  tne  interior  of  the  dry-pipe.  .The  ends  of  the 
pipe  are  capped.  The  nozzle  N  may  be  of  cast  iron,  cast  steel  or  pressed  steel.  Cast  iron  and  cast 
steel  nozzles  should  be  packed  with  a  copper  gasket  when  riveting  to  place,  this  copper  is  then 
swaged.  The  pressed  steel  nozzle  B  needs  no  copper  gasket. 

26 


N 


rj^/sY/ ///// /////////////////////// ////sj 

\  >  ^ 

f?22 Ey/V,^ 

•/AV<-^VVVT-V^V^'v^  V\W  ^V\<.VVVV.k.'l.^W^^^< 


Sec.A-B. 


FIG.  25. 


Steam  Nozzle: — The  formula  for  calculating  the  diameter  of  the  steam  nozzle  is 


A  = 


144 


where  ^  =  area  of  opening  in  square  inches. 

V  =  Vol.  of  steam  in  cu.   ft.  per  minute  passing  through. 
C  =  velocity  of  flow  in  F.  P.  M. 

Ordinarily  the  velocity  of  steam  is  taken  at  6000  F.  P.  M.  This  figure  might  be  approached  in 
short  pipes  or  even  in  cylinder  ports,  but  it  is  too  large  to  use  on  a  long  steam  pipe.  The  value  of  C 
should  be  between  2000  and  3000  for  the  steam  nozzle.  The  volume  of  steam  in  cubic  feet  per 
second  is 

H.  P.  X  30  X  5 


V  — 


60 


where  S  =  specific  volume  of  steam  at  boiler  pressure. 


The  size  of  the  steam  outlets  should  vary  by 
half  inches.  A  typical  steam  nozzle  is  shown  in 
Fig.  26.  When  made  of  cast  iron  it  should  be  de- 
signed very  heavy.  Cast  steel  is  preferred. 

Feed  Pipe: — Figure  the  diameter  d'  from  the 
same  general  formula  as  the  steam  outlet,  using 

5*  =  specific  volume  of  water  = 


62.4 


Fir,.  26.  It  is  always  well  to  have  a  large  water  inlet 

because  of  the  tendency  to  lime  up.  After  calcu- 
lating the  diameter  by  the  formula,  the  next  largest  standard  pipe  should  be  taken.  These  figures  are 
suggested  for  boilers  not  exceeding  150  H.  P. 

Enter  the  feed  pipe  into  the  boiler  by  flange 
fitting  according  to  the  H.  S.  B.  &  I.  Co. 

Blow-Off  Pipe: — -The  following  empirical  for- 
mula is  suggested  for  the  blow-off. 


H.  P. 
60 


+ 


FIG.  27. 


Attach  the  blow-off  according  to  Fig.  27. 


27 


WATER  TUBE  BOILERS. 

Very  little  data  can  be  given  on  the  design  of  water  tube  boilers.  The  types  from  the  various 
manufacturers  differ  so  widely  tnat  rules  for  design  can  be  given  only  in  the  most  general  way.  The 
boilers  are  built  up  in  most  cases  with  one  lower  drum  and  one  or  more  upper  drums  connected  by 
tubes  as  shown  in  Hutton  .bigs.  307-389.  \Vater  Circulates  from  one  drum  to  the  other  through 
the  tubes.  It  is  very  desirable  therefore  that  the  tuoes  have  a  good  free  passage  and  that  their  ar- 
rangement be  such  as  to  give  a  good  natural  draft.  The  water  line  of  the  boiler  is  generally  about 
the  center  of  the  upper  line  of  drums. 

Steam  Pressure: — The  steam  pressure  varies  from  150  to  200  pounds  gauge.  The  latter  figure 
may  be  accepted  in  this  design. 

Heating  Surface  and  Grate  Surface :— Water  tube  boilers  are  designed  for  10  square  feet  of  heat 
ing  surface  per  horse  power.  This  is  measured  on  the  fire  side  and  refers  to  all  surfaces  having  heat- 
ed gases  on  one  side  and  water  011  the  other. 

In  the  Stirling  boiler  this  includes  the  tubes,  all  the  lower  drum  and  half  the  upper  drum  ex- 
cepting the  ends  of  each  drum,  while  in  the  Wickes  boiler  it  includes  the  upper  part  of  the  lower 
cylinder,  all  the  tubes  and  about  two-thirds  of  the  surface  in  the  upper  cylinder. 

After  deciding  upon  the  type  of  boiler  to  be  designed  the  brick  work  must  be  planned  around 
the  steel  work  and  the  heating  surface  can  then  be  proportioned  to  the  various  parts.  The  following 
ratios  may  be  used: 

Heating  surface  per  H.  P 10.     n' 

Grate  surface  per  H.  P 33^' 

Ratio  of  H.  S.  to  G.  S 30.3 

Water  evaporated  per  square  foot  of  H.  S.  per  hour  from 

and  at  2i2°F 3.45  Ibs. 

Commercial  Rating  and  Horse  Power:— See    same  under  Multitubular  Boilers. 

Materials: — See  Multitubular  Boilers. 

Tubes : — Water  tubes  in  a  boiler  are  usually  larger  than  the  fire  tubes  in  a  multitubular  boiler 
of  the  same  capacity.  The  size  most  often  used  being  4  inches  outside  diameter.  From  90  to  96 
per  cent,  of  all  the  heating  surface  is  in  the  tubes,  the  latter  figure  applying  to  the  Wickes  boiler. 
Find  the  length  of  the  tubes  by  locating  the  drums,  and  from  this  obtain  the  number  of  tubes. 

Steam  and  Water  Drum: — Find  the  thickness  of  the  drum,  as  in  figuring  the  multitubular 
shell,  and  plan  for  the  least  number  of  riveted  joints. 

In  the  horizontal  type  of  boiler  the  drum  ends  are  dished  or  bumped  to  a  radius  equal  to  the 
diameter  of  the  drum,  and  do  not  need  staying.  In  the  vertical  type  the  heads  on  both  the  upper 
and  the  lower  drums  should  be  stayed  with  through  stays.  The  number  of  stays  is  estimated  by 
allowing  full  pressure  on  all  the  head  excepting  the  outer  two  inches  which  is  supported  by  the  shell. 

Headers : — In  the  horizontal  boiler  the  ends  of  the  tubes  are  expanded  into  steel  headers, 
which  in  turn  make  direct  water  connections  with  the  drums.  These  headers  are  made  of  sheet 
steel,  and  are  thoroughly  stayed.  In  the  vertical  boilers  the  tubes  are  expanded  into  the  inner 
drum  heads  themselves. 

Manholes  and  Handholes  are  placed  in  the  ends  of  the  drums  in  the  horizontal  type,  or  in  the 
bottom  of  the  lower  drum  in  the  vertical  type.  For  sizes  of  plates,  crabs,  etc.,  see  "Ryerson's  Month- 
ly Journal  and  Stock  List." 

Dry  Pipe  or  Baffle  Plate: — A  dry  pipe  is  well  adapted  to  a  water  tube  boiler,  but  a  baffle  plate 
is  sometimes  used  instead.  When  a  baffle  plate  is  used  it  can  best  be  located  near  the  rear  end  of 
the  upper  drum  so  as  to  take  steam  from  a  point  where  it  is  free  from  currents  and  consequently 
contains  less  moisture. 

The  steam  nozzle  should  be  located  near  the  center  of  the  upper  drum.  For  notes  on  nozzles 
and  steam  pipe  see  Multitubular  Boilers. 

Boiler  Setting: — The  headers  in  all  water  tube  boilers  either  rest  directly  upon  or  are  swung 
from  I-beams  which  are  built  in  the  side  brickwork.  Where  the  header  is  above,  a  set  of  rollers  is 
placed  between  the  header  and  the  I-beam  to  give  easy  expansion.  Where  it  is  below,  the  hanging  is 
flexible  enough  to  allow  for  expansion  without  interfering  with  the  brickwork. 

Baffle  walls  are  inserted  in.  the  boiler  setting  to  direct  the  gases  along  the  tubes.  Bolts,  buck 
staves  and  fronts  are  used  as  in  the  average  boiler  setting. 

Regulation  in  Boiler  Design: — Boilers  of  the  U.  S.  Navy  are  made  according  to  government 
rules  and  regulations,  known  as  "General  Rules  and  Regulations  Prescribed  by  the  Board  of 
Supervising  Inspectors  of  Steam  Vessels."  These  rules  are  printed  in  phamplet  form  and  may  be 
had  for  the  asking.  In  Great  Britain  the  same  is  under  the  control  of  the  British  Admiralty.  The 

28 


German  Lloyd  line  of  steam  vessels  have  their  own  rules.  In  stationary  work,  however,  no  such 
regulations  exist  and  the  proportioning  of  the  boiler  parts  is  left  entirely  with  the  designer.  When 
the  boiler  is  ready  for  use  it  is  insured  by  some  representative  insurance  company,  and  reinsured  at 
stated  intervals  during  use.  The  largest  company  in  the  United  States  is  the  Hartford  Steam  Boiler 
and  Insurance  Company,  which  publishes  a  paper  called  "Locomotive,"  containing  a  record  of  boil- 
er explosions  and  other  information  valuable  to  the  trade.  Representative  companies  in  England 
are  the  Vulcan  Insurance  Company  and  the  Manchester  Steam  Insurance  Association. 


29 


GAS  ENGINE   DESIGN. 

(Arranged    oy  C.  S.  JOHNSON.) 

Problems : — Work  up  a  set  of  problems  on  trie  same  general  lines  as  those  under  Steam  Engine 
Design. 

Indicated  Horsepower:— The  ratio  of  ]',.  H.  P.  to  I.  H.  P.  in  gas  engines  will  be  taken  at  .8  in  the 
larger  to  .7  in  the  smaller  engines. 

Let  P  -  -  M.  E.  P.  in  pounds  per  square  inch  for  the  working  stroke. 
L,  —  length  of  stroke  in  feet. 
a    =  effective  area  of  piston  in  square  inches. 
W  =  R.  P.  M. 

n    ••  -  explosions  or  impulses  per  min. 
S  -  -  piston  speed  in  F.  P.  M.  assuming    velocity  constant  at  all  points  of  the  stroke. 

Then  I.  H.  P.  =     PLan 
33000 

'    N  t      t 
n  = for  four-cycle  engines. 

n  =  N  for  two-cycle  engines. 

Equation  (21  )gives  the  I.  H.  P.  for  one  cylinder  (single   acting).      For   other   combination   of  cylinders 
and  for  double-acting  engines  proper  factors  must   be  introduced. 

Piston  Speed:— S  =  2LNorLN=—  ,  Then  (21)  becomes  I.  H.  P.  =  •    (22) 

2  4  X  33000   v 

for  a  single  acting  four-cycle  engine. 

and  (21)  becomes  I.  H.  P.  =    — — —        •    for  a  single  acting  two-cycle  engine.  (23) 

The  following  table  gives  values  representing  the  limits  of  piston  speeds  used  in  practice  and 
which  vary  slightly  from  steam-engine  practice. 

I.  H.  P.  S  =  F.  P.  M.. 

looo   Stationary    700  to  looo  800  Average. 

700  "  700  "  800  750 

500  "  650  "  850  700 

150  "  ..600  "  800  650 

50  " 500  "  700  600 

Small  450  "  700  550 

2-10  H.  P.  per  cyl.  (Automobile) 600  "  1000  750 

Compression  Pressure  and  M.  E.  P. : — High  compression  permits  of  easy  ignition  of  weak  gas 
which  would  not  burn  in  the  open  air  and  this  makes  it  possible  to  use  a  very  weak  fuel,  hence  giving  more 
work  from  a  given  amount  of  fuel,  that  is,  better  economy.  High  compression  also  gives  a  correspond- 
ingly increased  M.  E.  P.  so  that  from  the  point  of  economy  and  power,  high  compression  is  to  be  ad- 
vised. 

Compression  will  vary  with  the  fuel,  speed,  manner  of  cooling,  etc.,  and  is  difficult  to  predict  with 
any  degree  of  certainty,  however,  a  few  fuels  and  their  compression  pressures  obtained  in  practice  will 
be  given. 

30 


Gasoline. — Compression  varies  from  45*[!"  to  95*""  gauge,  with  an  average  of  6^".  In  auto- 
mobiles the  compression  pressure  is  sometimes  kept  low  to  permit  easy  starting.  In  slower  speed  en- 
gines with  better  cooling,  compression  will  vary  from  6o$[]"  to  85*[1",  with  an  average  of  7O#n". 

Kerosene. — Small  engines  running  from  250  to  500  R.  P.  M.  compression  will  vary  from  30*""  to 
75#[]"  and  with  independent  vaporizers  compression  will  vary  from  45*[I"  to  85#[1",  with  an  average  of 


Cit\  Gas. — In  small  engines,  compression  varies  from  6o*[1"  to  ioo*[I",  with  an  average  of  8o#[1". 

Natural  Gas. — For  medium  and  large  engines  with  good  cooling,  compression  ranges  from  75#[1" 
to  I3of[1",  average  115*"". 

Produce!    Gas. — Compression  varies  from   ioo*[1"  to  i6ot[1". 

Blast  Gas. — Used  in  large  engines  and  takes  compression  at  from  I2o5[1"  to  iyo*[1",  average 
i55*[]". 

M.  E.  P.: — As  the  M.  E.  P.  depends  upon  compression,  mixture,  etc.,  its  determination  involves  an 
expression  whose  use  is  laborious.  Fig.  28,  gives  the  relation  between  M.  E.  P.  and  compression  pres- 
sure directly  without  calculation. 

Theoretical  Indicator  Cards: — Having  determined  the  principal  dimensions  of  the  proposed  en- 
gine the  first  thing  to  be  done  is  to  construct  the  Theoretical  Diagram  Sheet.  As  an  illustration 
of  these  a  set  of  four-cycle  engine  diagrams  will  be  constructed.  Fig.  30. 


105 

30 
8»- 

§-7.5 

cr 

<3~ 

etc 

<o 

-Q- 
545 

QL 
k-1 


13 


30      45       tO       75      SO      I05s 

Gompre  55ion-lfoi  tyer  aq  m  ^ 

Fir,.  28. 


400 
<3fcO 
320 
280 
'240 
200 
IbO 
120 
80 
40 

200 
180 
IfcO 
140 
120 
100 
80 

to 

40 

| 

\ 

\ 

\ 

* 

n 

\ 

\ 

\ 

\ 

\ 

\ 

X 

\ 

\ 

\ 

'• 

\ 

s 

p 

\ 

\ 

\ 

\ 

s 

s 

V 

\ 

l\ 

"*v 

x 

S 

\, 

*-^. 

*-*. 

•^-» 

V 

—  . 

-^ 

-—  —  . 

*^*. 

•  — 

~»— 

^TT. 

•—ii. 

-----  1 

— 

B20 

r> 

s 

5        b       7 

FIG.  29. 


10 


To  do  this  one  of  the  following  factors  must  first  be  determined,  namely,  cylinder  volume  ratio 
or  compression  pressure  ;  in  order  to  make  use  of  Fig.  29  in  which  the  crdinates  represent  absolute 
pressures  in  pounds  per  square  inch  and  the  abscissae  represent  the  total  cylinder  volumes. 

4 

The  curves  A  B,  C  D  and  E  F,  follow  the  law  P  V^  =  C  which  comes  nearest  the  average  prac- 
tice. 

The  curve  A  B  gives  the  relation  between  volume  and  pressure  during  compression  and  is  read 
by  the  scale  to  the  right  of  the  figure.  Curve  C  D  is  the  same  as  A  B  but  is  plotted  to  the  scale  at  the 
left.  Curve  E  F  gives  the  relation  between  volume  and  pressure  after  the  charge  has  been  ignited 
and  is  plotted  to  the  scale  to  the  left. 


31 


& 

N 

\ 

Spring  Ho" 

f    ^ 

*  ^5    ~m 

\ 

^ 

<o       c 

iJO 

£ 

$ 

I 

\ 

I 

^H 

s 

6 

' 

a, 

*5 

*—  V—  ' 

^ 

^ 

•  —  ^ 

£•^1 

•^^ 

^CS 

V 

/ 

Theoretic*! Iff(/icator  Card. 


Inertia 


P/sfon 
Position 

Values  of  H£ 

ft 
TT  - 

/ 

ZT 

i 

3 

ijr 

1 

3 

i 
n 

.00 

00 

00 

.00 

ao,.oo 

•OS 

47 

as 

50 

.50  [50 

.10 

{,<> 

.6S 

tf 

tj$o 

•ZO 

S4 

8h 

88 

90i9Z 

.30 

Stf 

36 

98\i,fl\/.M 

&o 

1.01 

1.01 

IC3W 

LOB 

.JO 

1.01 

1.01 

lOmO* 

1.0k 

•to 

97 

91 

96  bs 

I.DO 

.70 

86 

SI 

85  [g9 

89 

.80 

n 

.74 

,?Z 

74 

.74 

.90 

54 

5^ 

.50 

52 

SO 

35 

39 

.13 

,U 

.37 

34 

I.O 

Off 

.00 

oo 

00 

X>0 

\ 

\ 

.03- 

\ 

/ 

\ 

"  — 

~.^~ 

w 

j 

• 

1 

ti 

* 

!J 

.1 

i 

J 

/» 

^ 

,^-^ 

I.O 

00 

.00 

ao 

J}0 

£0 

.1 

$~ 

.9 

e 

.7 

< 

.s 

4 

3 

2    i 

01 

^  —  ' 

';, 

SI, 

«  —  ..  -  Fytilfl'iinn               . 

. 

.  —  - 

r 

v/;/ 

7/^< 

f 

-  ^ 
?— 

—— 

^^- 

?ll 

ffl 

in 

r 

—  —  ' 

im 

hn 

"•f5 

inr 

~- 

-  '•>          Wrist  Pin  Pressure  Biaqrain 


r   T~ 

'  f  t£=E 

'  k  P 

»   W 

f°        t" 

.?        JB 

r 

4 

i  . 
A    •?• 

J 

1 

| 

or 

1 

fa 

!    I         i 

ction  —  

ll 

r^ 

^7^1 

rf 

i  «;;/»» 

1 

%%%2Zs                  ~T?              .-- 

C 

1 

!*- 

r> 

\(C\              ;  \!,-\               "wH\  —  "'  ^"  "~':\-K!> 

... 

;3 

0 

1 

v>—  '  ,                      ;  ••—                       .u^l         ,     1         Jf{2! 

V            •"  : 

,.  ..  ,.                  \                           *                  > 

,, 

FIG.  31. 

Volume  Ratio  is  the  relation  of  clearance  volume  to  that  of  exhaust,  that  is,  volume  ratio  =  • 

v 

Fig.  31.    As  an  example  take-r^-  =  =  .28  this  gives  a    compression    pressure     of     8o#[I"  abs   (Fig.  29 

scale  to  right)  and  an  explosion  pressure  of  27O#[1"  abs   (scale  to  left).     If  the  compression  pressure 
was  known  and  it  was  desired  to  find  the  volume  ratio,  the  above  process  would  be  reversed. 

The  theoretical  card  would  be  formed  then  by  the  lines  C  d  (compression),  d  e  (explosion)  e  F 
(expansion),  and  F  C  (exhaust),  all  pressures  being  read  by  the  lefthand  scale.  The  area  inclosed 
in  this  card  represents  the  work  done  per  working  stroke. 

Accelerating  Force  and  Inertia  Cards: — The  accelerating  force  taken  up  and  given  out  by  the 
reciprocating  parts  each  stroke,  is  given  by  the  following  formula  for  the  development  of  which  see 
Young's  Steam  Engine  and  Boiler  Notes. 


jj/  y,      .  sin2  e  L-  cos'  e       . 

F  =  32T2*   (^Vl^^'e  +*'(£-.in«e)0 


(24) 


where  F  =  accelerating  force. 
6    =  crank  angle. 
V  =  velocity  of  crank-pin  in  F.  P.  5". 
IV  =  weight  of  reciprocating  parts  in  Ibs. 
R  =  length  of  crank  in  feet. 
When     8=0  the  crank  is  on  head-end  dead-center  and  equation  24  becomes 


wv- 


+ 


32.27? 
and  when    0  =  180°  the  crank  is  on  crank-end  dead-center  and  equation  24  becomes 


F  =  — 


wv- 

32.2  R 


R 


(25) 


(26) 


F  will  be  equal  to  zero  when  the  crank  and  connecting  rod  are  at  right  angles,  i.  e.,  when  the  piston 
has  attained  its  maximum  speed.  The  distance  the  piston  is  from  the  head-end  when  at  its  maximum 
speed  will  be  found  as  follows : 

Let  Q  Fig.  32,  be  the  piston  position  when  R  and  L  are  at  right  angles  and  let 

A—  i/  p  —  NK 

L  2 

Then  N  Q  =  A  N  —  A  Q 

=  (£,  +  /?)_  V 


FIG.  32. 


+  R2 


N  Q 
-  .44  N  K  or      -~=  -44 


F  in  equation  24  is  the  total  accelerating  force  in  pounds  necessary  to  accelerate  the  reciprocat- 
ing parts  but  as  the  inertia  curves  are  to  be  combined  with  the  theoretical  indicator  cards  whose 
ordinates  are  in  pounds  per  square  inch,  the  ordinates  of  the  inertia  curves  should  be  in  the  same  units. 

33 


Therefore  if  we  divide  both  sides  of  equation  24  by  a,  the  area  of  the  piston,  we  get  the  ordinates 
of  the  inertia  cards  to  the  proper  scale.  To  find  the  value  of  F  -=-  a  in  equations  25  and  26  involves 
a  knowledge  of  W  -r-  a,  the  weight  of  the  reciprocating  parts  per  square  inch  of  piston  area. 

Fig.  33  gives  the  relation  between  the  weight  ot 
the  reciprocating  parts  per  square  inch  of  piston 
area  and  the  diameter  of  the  cylinder  and  by  its  use 
the  weight  of  the  reciprocating  parts  can  be  es- 
timated if  the  cylinder  diameter  is  known. 

We  are  now  able  to  find  three  points  on  the 
inertia  diagram,  viz.  F  -=-  a  for   6   =  o,  F  -f-  a  when 
6     =  180°  and  when  F  -=-  a  =  o.    These  should  be  fc 
plotted  as  ordinates  on  a  base  line  corresponding  to  ^ 
the  stroke,  to  same  scale  as  theoretical  indicator  card.  | 


A  circle  struck  through  these  three  points  will  be 
a  very  close  approximation  to  the  true  inertia  curve.  • 

In  the  Inertia  Diagram,  Fig.  30,  F  -f-  a  for  6 
=  o  is  +  57.6  pounds  and  P  -f-  a  for  6  =  180°  is 
-  34.5  pounds.  F  -=-  a  =  o  at  .44  stroke. 

It  will  be  noted  that  in  this  discussion  the  force 
that  accelerates  the  reciprocating  parts  from  o  to 
their  maximum  i.  e.,  when  they  are  taking  up  energy, 
was  called  positive  (-)-)  while  the  force  given  out 
as  the  reciprocating  parts  are  retarded  was  called 


10  IS  ZO  25  iO 

of  Cylinder  in  Inches. 

FlG-  33- 

negative  ( — ) .  In  order  to  accelerate  the  reciprocating  parts  this  accelerating  force  must  come  from 
the  gas  pressure  behind  the  piston  and  from  the  gas  pressure  standpoint  must  be  viewed  as  a  negative 
force  and  on  the  other  hand  when  the  reciprocating  parts  are  being  retarded  they  give  out  their  stored 
up  energy  and  exert  a  helpful  influence  and  from  the  gas  pressure  stand  point  must  be  said  to  be  pos- 
itive. This  will  be  made  clear  by  a  study  of  Figs.  34  and  35. 

Let  P,  =  Pressure  along  connecting  rod.     T  = 

P 


Tangential  pressure  producing  rotation.  P  t  = 
cos  $ 


T  =  P->  cos  $  =  P  • 


cos 


COS  ft 

(27) 


FiG.  34. 

PE  =  Explosion  pressure. 

Pl    =  Force  necessary  to  accelerate  reciprocating  parts. 
Then  from  Fig.  34,  P  =  PE  —  Pl    =  Pressure  on  wrist-pin. 
In  Fig.  35,  P  =  PE  +  Pl 


Wrist  Pin  Pressure  Diagram: — The  theoret- 
ical indicator  card,  Fig.  30,  gives  the  gas  pressure 
acting  on  the  piston  at  any  instant,  and  from  the 
inertia  card  can  be  gotten  the  force  of  inertia  acting 
at  the  same  instant.  Combining  these  we  obtain  the 
wrist  pin  pressure  diagram  giving  the  force  at  the 
wrist  pin  available  for  producing  rotation  of  the 
crank.  These  are  plotted  to  a  four  stroke  base. 


Fie.  35- 


Tangential  Pressure  Diagram: — If  we  multiply  the  ordinates  of  the  wrist-pin  pressure  diagram 
by  the  values  of  A  N  -f-  R  for  the  different  crank  positions  corresponding  to  the  proper  piston  positions 
and  plot  on  a  base  circle  whose  diameter  is  equal  to  the  stroke  we  obtain  the  tangential  pressure  dia- 


L  are  given  in  the  table.  Fig.  30. 


gram. 

The  values  of  A  N  -4-  R  for  several  values  of  R 

Rectified  Tangential  Pressure  Diagram: — Changing  from  polar  to  rectilinear  coordinates  gives 
the  Rectified  tangential  pressure  diagram. 


34 


Mean  Tangential  Pressure : — Since  the  first  or  explosion  stroke  of  the  indicator  diagram  and  the 
derived  diagrams  are  all  work  diagrams  their  areas  should  be  equal  and  proportional  to  the  work  done 
by  this  stroke. 

Let  M.  E.  P.  =  Mean  Effective  Pressure  =  P. 
M.  T.  P.  =  Mean  Tangential  Pressure. 

a  =  Area  of  piston  in  square  inches. 
L  =  Length  of  stroke  in  feet. 

Since  the  M.  E.  P.  for  the  theoretical  indicator  card  is  the  M.  E.  P.  for  the  working  stroke  only, 
the  mean  driving  pressure  for  the  four  strokes  or  two  revolutions  is  P  -f-  4.  Then  P  -=-  4  X.4  L  1S 
an  expression  for  the  work  done  in  the  cylinder  and  M.  T.  P.  X  2  v  L  =  work  done  at  the  crank-pin, 
but  if  we  neglect  friction,  the  work  done  in  the  cylinder  is  equal  to  the  work  done  at  the  crank-pin. 

.  •.  P  -=-  4  X  4  L  —  M.  T.  P.  X  2  TT  L  or  M.  T.  P.  =  P  -=-  2  w.  (28) 

This  M.  T.  P.  is  indicated  on  the  rectified  tangential  pressure  diagram  by  the  ordinates  of  the 
long  narrow  unshaded  portion.  This  diagram  gives  at  once  the  relation  between  maximum  and  mean 
turning  force,  in  this  case  tangential  pressure  (max.)  -f-  M.  T.  P.  =  8.9  which  is  available  for  crank- 
shaft design. 

It  also  gives  the  relation  of  the  maximum  energy  delivered  A  £  to  the  mean  energy  E 
which  is  a  measure  of  the  weight  of  fly-wheel  necessary  to  limit  the  angular  velocity  variation  during 
each  cycle.  This  is  the  ratio  of  the  shaded  portion  to  the  long  narrow  unshaded  portion  and  in  this 
case  is  A  £  -=-  £  =  1.61  -f-  1.68  =  .96. 


ENGINE   DIMENSIONS. 

Cylinder:  —  The  cylinder  when  not  too  thick  is  subjected  to  simple  tension  due  to  internal  pressure 
which  may  be  taken  at  4508""  max. 

Length:  —  The  length  of  cylinder  will  depend  upon  piston  length,  stroke,  clearance,  etc.  Pistons 
usually  project  beyond  their  cylinders  when  single-acting  and  where  short  frames  are  desired. 

Water  Jacket  :  —  All  parts  of  cylinder  exposed  to  the  hot  gases  should  be  water  cooled  except  on 
very  small  engines.  The  water-jacket  should  extend  beyond  the  piston  travel  a  short  distance. 

The  amount  of  water  should  be  sufficient  to  carry  off  50%  of  the  heat  developed.  Another  method 
is  to  let  the  jacket  take  care  of  two  times  as  much  heat  as  is  converted  into  work.  Thus  for  a  25  H.  P. 


engine  the  jacket  should  care  for  -         --  <r—  '  B.  T.  U. 

Water  Space:  —  The  water  jacket  should  be  free  from  pockets  and  of  such  shape  that  free  circula- 
tion will  result.  Let  u\  =  width  of  water  space  then  u\  =  .06  d  for  horizontal  cylinders.  For  vertical 
cylinders  it\  is  less  than  this  amount.  For  a  thin  swift  stream  w^  will  be  made  less,  say  wt  = 
.045  d  and  for  large  cylinders  K\  =  .15  d. 

Jacket  Walls:  —  The  jacket  walls  should  be  designed  to  carry  an  internal  water  pressure  of  508"' 
also  to  support  the  parts  of  the  mechanism  and  to  take  the  weight  of  the  cylinder  when  horizontal. 

For  small  automobile  engines,  thickness  of  walls  ^  =  .06  d.  For  slow-speed  stationary  engines 
ft  =  .10  d  and  where  reinforced  tl  =  .05  d. 

Valves:  —  Valves  are  of  two  general  types,  flat  and  conical.  Gases  should  enter  and  leave  the 
cylinder  with  as  little  expenditure  of  energy  as  possible.  To  obtain  the  best  results  suction  should  take 
place  as  little  below  atmosphere  as  possible  and  exhaust  should  take  place  as  little  above  atmosphere  as 
possible.  These  pressures  will  depend  upon  the  piston  speed  and  valve  opening.  The  valve  lift  should 
bear  a  constant  relation  to  the  piston  speed  in  order  that  velocity  of  the  gas  through  the  valve  be  uni- 
form. 

Size:  —  The  size  of  valve  depends  upon  speed  of  the  piston.  The  inlet-valve  should  be  of  such 
size  that  the  mixture  at  atmospheric  pressure  should  have  a  velocity  of  about  100  F.  P.  S.  and  exhaust- 
valves  such  as  to  give  a  velocity  of  about  85  F.  P.  S.  For  small  high-speed  engines  these  velocities  will 
be  somewhat  greater. 

35 


Both  inlet  and  exhaust  valves  are  often  made  the  same  size,  however,  and  vary  in  diameter  from 
A  =  .3  d  to  .45  d. 

Valve  Lifts:  —  Valve  lifts  will  vary  from  /^  —  .05  A  to  .1  A  for  flat  valves  and  h^  =  .07  A  to  .16 
A  for  conical  valves,  where  A  is  the  diameter  of  the  valve  opening  in  the  seat,  called  valve  diameter. 

Thickness:  —  Valves  when  small  are  made  of  flat  discs,  when  large  are  arched  and  are  water- 
cooled.  Flat  valves  are  treated  as  plates  supported  at  the  edges  and  uniformally  loaded  for  which 
Grashof  gives 

1  (29> 


-  V*®1 


where  T  =  valve  thickness. 

A  =    diameter   of   valve   under   unbalanced  pressure. 
/  =  fibre  stress  of  metal. 
Pm    =  maximum  pressure  in  #[]". 

Small  engines  have  valve  thickness  of  from  T  =  .09  A  to  .23  A  which  corresponds  to  a  fibre 
stress  of  from  f  =  25  Pm  to  f  --  4  Pm.  The  latter  value  gives  a  very  stiff  valve,  one  that  will 
not  spring  or  leak. 

Flat  valves  have  faces  varying  from  f  =  .04  A  to  .09  A.  Conical  valves  have  faces  of  from 
I.I  to  1.5  times  width  of  seat.  The  normal  pressure  on  cone-seated  valves  can  be  taken  at  P'  = 
•\/2  Pv  =-  1.41  Pv  (for  45°  valve)  where  P'  =  normal  pressure  and  Pv  =  pressure  on  valve. 

For  small  engines  •  width  of  cone-seats  vary  from  .09  d  to  .  1  5  d  while  for  larger  engines  the  seats 
vary  in  width  from  .06  d  to  .1  d.  Outside  diameter  of  valve  should  be  large  enough  to  permit  the  face 
to  overlap  the  seat. 

Valve  Stems:  —  Exhaust  valve  stems  must  be  strong  enough  to  lift  the  valve  against  a  terminal 
pressure  of  from  2.2  to  6.5  atmospheres.  This  latter  being  found  in  automobile  engines  of  spark  con- 
trol type.  For  stationary  work  a  value  of  508""  can  be  used.  Stems  of  a  free  length  exceeding  15 
diameters  are  treated  as  columns  under  flexure.  The  length  of  the  stem  bearing  will  vary  from  1.4 
A  to  3.5  A  Diameter  of  stems  vary  from  .22  A  to  .28  A 

Valve-Closure  Springs:  —  Helical  coil  springs  are  used  almost  universally.  From  8  to  15  coils  or 
turns  are  used  on  cam  operated  valves  and  from  5  to  6  on  automatic  valves. 

Let  W&   =  force  (assumed  constant)  necessary  to  close  valve  in  a  given  time  (t). 
iv   =  weight  of  valve. 
h  =  valve  lift  in  inches. 
a  =  acceleration. 
V  =  velocity  in  F.  P.  S. 
S  -  =  space  passed  over. 
The  weight  w  must  move  through  h  -~  12,  feet  in  t  seconds. 

V=—  (30) 

and  S=  y2  af~  (31) 

From  30  and  31  we  get  V  =  ~  =  ^~ 

inches  per  sec2,  and  Ws  =  __  w  h  (32) 

r  *  ft    1  \S    £    a    -    Ifl7     O     ./      <2  v        > 


6/2  32. 2  X  6/2-193.2,< 


or  t  =  .072  J  h  ._  —  time  in  seconds  neglecting  friction. 


The  spring  should  be  capable  of  closing  the  valve  in  *4  of  a  stroke  or  y&  revolution.  This  was 
found  by  Mr.  H.  L.  Towne  to  be  the  maximum  time  required  in  a  series  of  experiments  with  automatic 
valves  on  automobile  engines. 

Let  N  —  R.  P.  M.then  one  revolution  will  take  60  -+-  N  seconds  of  time  and  the  time  of  closure 
of  valve  will  be  t  =  60  -f-  8  Ar  or  t2  =  56.25  -=-  N-  (33) 

and  from  32  and  33  we  get  for  l/\  stroke  closure  Ws  =  w  h  N2  ~-  10867.5  (34) 

For  automatic  or  vacuum-opened  valves  the  spring  tension  will  vary  from  6  to  30  ozs.  per  sq.  in. 
of  valve  area  with  average  of  12  oz.  or  .75  pounds. 

For  mechanically  operated  valves  Ws  should  always  be  figured  by  equation  34  and  should  give 
values  that  will  be  between  Wa  =  5.5  wA.2 _-=-  4  to  9  ?r  A2  -f-  4. 

In  the  selection  of  springs  there  is  a  wide  range  of  dimensions  the  only  limitations  being  (i)  a  cer- 
tain minimum  load,  (2)  no  practical  change  in  load  for  the  required  valve  lift. 

36 


Cams : — The  cams  should  be  so  designed  that  the  lift  at  all  times  is  proportional  to  the  piston- 
speed  with  such  exceptions  as  are  pointed  out  in  Lucke's  Gas  Engine  Design,  Cuts  102  to  no. 

Timing: — Inlct-Valres  should  not  open  until  exhaust  valves  are  closed.  If  exhaust  closes  on  cen- 
ter or  a  little  later  the  inlet-valves  should  open  still  later. 

Engine.                                                            Inlet  opens.  Inlet  closes. 

Large  slow-speed                                             about  5°   after  center  about  10°  after  center. 

Medium  or  slow-speed  small                         about  3°   after  center.  about    4°  after  center. 

Small  high-speed                                             about  6°   after  center.  about  15°  after  center. 

Exhaust  Valves  should  open  early.  The  amount  of  advance  depends  upon  speed,  diameter  of 
valves,  etc. 

Engine.                                                       Exhaust  opens.  Exhaust  closes. 

Slow  speed                                                        about  25°    before  center.  On  center. 

Small  high-speed                                             about  35°   before  center  2°  after  center. 

Piston,  Piston  Heads : — Piston-heads  are  treated  as_flat  plates  supported  at  the  edges  and  uniform- 
ally  loaded,  for  which  Grashof  gives 

r-.rf^  «/-*£-  (35) 

in  which  T  =  thickness  of  piston  head  in  inches. 
d  =  diameter  of  piston  in  inches. 
f  =  fibre  stress. 

Pm  =  max.  pressure  in  cylinder. 

Engines  of  diameter  under  6  inches  usually  have  flat  unstayed  heads  varying  from  T  •  -  .04  d  to 
.08  d  with  an  average  of  T  =  .06  d.  Where  lightness  is  a  factor  (automobiles)  piston-heads  as  thin 
as  Y&  inch  are  successfully  used.  Engines  of  diameter  over  6  inches  should  be  web-stayed  for  stiffness. 
Where  arched-heads  are  used  the  thickness  can  be  reduced  to  .6  T.  Webs  are  usually  .6  T. 

Length — In  single-acting  engines  the  wrist-pin  is  carried  in  the  piston,  this  produces  a  rubbing 
on  the  sides  of  the  cylinder  clue  to  the  side  thrust  of  the  connecting-rod.  The  piston  length  must  be 
sufficient  to  reduce  this  to  a  minimum. 

Max.  pressure  on  head  =  Pm  IT  d~  -i-  4. 
Max.  pressure  on  guide  =  Pt  ?r  d1  -j-  4. 
But  P1  =  Pm  tan>  (max.)  Fig.  35. 

where  P1  =  =  Pressure  on  guides  or  between  piston  and  cylinder. 
Pm  =  Max.  pressure  on  piston. 

ft  —  Angle  between  connecting-rod  and  center-line  of  engine. 

If  L  =  length  of  piston  and  d  =  diameter,  then  the  projected  area  =  L  X  d  to  receive  the  maximum 
guide  pressure  Pj. 

Then  P,  =  -^  X  .P-tan^nax.}  ^ 

4  ^  X  a 

In  practice  Pl  will  run  from  4  to  22#[1"  and  the  length  will  run  from  Z,  =  </  to  Z,  =  1.6  d  for  high- 
speed engines.  For  small  stationary  engines  L  =  1.4  d  to  2.3  d  and  for  large  stationary  engines  L  = 
1.2  d  to  1.7  d. 

Piston  Kings: — The  number  of  rings  vary  3  to  10.  A  clearance  of  about  .001  inch  is  allowed  at 
the  sides  to  prevent  sticking.  They  are  usually  made  of  C.  I.  being  thin  at  the  ends  and  thicker  in  the 
middle.  Original  diameter  of  rings  before  cutting  is  =  d  -\-  .175"  for  small  rings,  d  -)-  .25"  for  rings 
for  8"  to  1 8"  engines  and  for  very  large  rings  an  increase  of  .01  d  is  allowed.  The  width  will  vary 
from  *4"  to  j?4".  The  bridge  between  rings  varies  from  ^2  to  I1/?  times  the  width  of  ring. 

Wrist  or  Piston  Pin: — A  pressure  of  from  7508""  to  i2ooS[]"  projected  area  should  be  used.  Piston 
pins  are  figured  in  the  same  manner  as  wrist-pins  in  steam  engines.  (See  Steam  Engine  Notes.) 

Connecting  Rod: — (See  Steam  Engine  Notes).  Automobile  engines  usually  are  circular  and  mid- 
section  of,  d  =  .oil  D  V-Pm  to  d  =  .014  D  V-fm-  When  rectangular  and  of  a  thickness  t  and  depth  d. 
d  =  2.25  t  at  crank  and  d  =  1.5  t  at  wrist  pin. 

Cranks,  Shafts,  Pins  and  Cranks: — These  will  follow  the  design  for  similar  parts  in  the  steam- 
engine  (see  Steam  Engine  Notes).  A  pressure  of  400  to  5oo#[I"  can  be  allowed  on  crank  pins  and  from 
200  to  25o#[1"  on  crank  shaft  bearings. 

37 


Fly- Wheels :  Steadiness  of  Speeds — The  most  important  function  of  the  fly-wheel  is  to  maintain 
an  angular  velocity  within  certain  prescribed  limits  of  variation  throughout  the  c\cle.  This  we  will  call 
the  steadiness  of  speed.  Steadiness  of  speed  therefore  is  the  variation  of  speed  between  one  impulse 
and  the  next  and  is  dependent  only  on  the  energy  storing  power  of  the  fly-wheel.  Steadiness  of 
speed  is  not  the  per  cent  of  difference  of  speed  between  no  load  and  full  load,  a  mistake  often  made ; 
for  if  the  no  load  speed  was  220  R.  P.  M.  and  the  full  load  speed  was  212  R.  P.  M.  Then  220  - 
212  =  8  R.  P.  M.  and  8-r-  216  =  3.7%  which  is  not  the  coefficient  of  steadiness  of  speed.  The  revolu- 
tions per  mniute  are  controlled  entirely  by  the  governor. 

The  rational  method  of  calculating  the  stored- up  energy  of  the  fly-wheel  is  to  make  a  graphical 
diagram  of  the  changes  that  take  place  at  the  crank -pin  due  to  the  combination  of  gas  and  inertia  forces 
and  calculate  the  weight  of  fly-wheel  from  this  consideration.  Such  a  graphical  diagram  is  the  Rec- 
tified Tangential  Pressure  Diagram.  Fig.  30  and  the  coefficient  of  fluctuation  of  energy  is 

A  B  area  of  shaded  portion 
~" 


E          area  of  long  narrow  unshaded  portion 

From  Steam  Engine  notes  we  have  for  the  weight  of  the  fly-wheel  rim  W  =  K  B  g  -j-  «  V~. 
The  values  of  n   (coefficient  of  unsteadiness)    for  the  different  classes  of  work  are  given  below. 

For   Pumping  and   ordinary  duties   n  =  .05 

For  Driving  machine  tools  n  -.  .03 

For  Driving  textile  machinery  n  =  .025 

For  Driving  dynamos  n  =  .02 

For  Spinning  machinery  n  i  :  .01 

Marine  Engines  n  =  .15 

Automobiles  n  =  .335 


YE  05752 


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STAMPED  =arra 

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